Hi Minty,
In truth before researching this a bit, all I knew was that low vitamin D levels lower your immunity in general. Hence, if you happen to eat a bug (pathogen, stomach virus, bad bacteria, bad yeast, etc), you'd have lower immunity, and your body would be less likely to succeed over killing/removing/reducing the bug than if you had higher levels of vitamin D and other immunity vitamins/compounds. So, in short, you'd be a higher risk of getting a digestive infection contributing eventually to IBS or SIBO, but also you're more susceptible to catch other things like COVID, a cold, flu,etc.
Here' s the research i found from some quick google searches:
Hypothyroidism and SIBO link (academic research paper)
www.ncbi.nlm.nih.gov
A review of clinical studies asking about the hypothyroidism and SIBO link
kresserinstitute.com
Some website trying to offer solutions for people with both conditions:
rootfunctionalmedicine.com
" You can support optimal gut and thyroid health by eating regularly scheduled meals that are rich in dietary fiber, limiting added sugar, and supporting optimal digestion as needed with digestive enzymes, bile extract, and/or HCl." -- from rootfunctionalmedicine.com
From reading the first one from nih.gov it just seems to say, yes, people who have hypothyroidism are likely to get SIBO.
The second website (kresserinsitute), has much more information, and even at one point says that treating hypothyroidism led to worse SIBO.
FYI- I wouldn't recommend not treating hypothyroidism just to avoid worse SIBO.
To your question, from the research I was able to see from (15 mins) reading/scanning these, it doesn't seem that by treating your hypothyroidism, your SIBO would go away.
Almost all the websites acknowledged a need for antibiotic and probiotic treatment to treat the SIBO.
I've also checked out some reddit posts on SIBO, and in coordination to my own experience, a targeted 2 week treatment of SIBO (antibiotics, low/no sugar diet, plus probiotics) seemed to DRASTICALLY heal/fix/reduce gas symptoms in most people (including myself).
The thing is depending on how bad the situation is, its more about keeping it gas free in terms of being SIBO free.
IE you can get rid of gas quickly with the antibiotics and restrictricted sugars/starches. But if you decide to reconsume food for the bacteria too soon (before repopulating your gut with enough probiotic to overcome/overwhelm and dominate in your gut over the bad bacteria) then you just keep getting gas anyway.. ---That's what it seems from the reddit posts and also, this idea was hinted from my experience too. ---> On my first round of Xifaxan, I actually did need it everyday to reduce, when I forgot a day, the gas did come back (keep in mind, I was low/no sugar and taking probiotics). On my second round (a few months later), I must have repopulated enough that I only needed 2-3 days of Xifaxan and then I just kept the rest of the bottle at home for a gas emergency.
In truth before researching this a bit, all I knew was that low vitamin D levels lower your immunity in general. Hence, if you happen to eat a bug (pathogen, stomach virus, bad bacteria, bad yeast, etc), you'd have lower immunity, and your body would be less likely to succeed over killing/removing/reducing the bug than if you had higher levels of vitamin D and other immunity vitamins/compounds. So, in short, you'd be a higher risk of getting a digestive infection contributing eventually to IBS or SIBO, but also you're more susceptible to catch other things like COVID, a cold, flu,etc.
Here' s the research i found from some quick google searches:
Hypothyroidism and SIBO link (academic research paper)

Link between hypothyroidism and small intestinal bacterial overgrowth
Altered gastrointestinal (GI) motility is seen in many pathological conditions. Reduced motility is one of the risk factors for development of a small intestinal bacterial overgrowth (SIBO). Hypothyroidism is associated with altered GI motility. The aim ...
A review of clinical studies asking about the hypothyroidism and SIBO link
The Hypothyroidism-SIBO connection - Kresser Institute
The Hypothyroidism-SIBO connection . Find more Autoimmune Disorders, Thyroid Disorders articles on Kresser Institute

Some website trying to offer solutions for people with both conditions:

SIBO and Hypothyroidism
SIBO and hypothyroidism commonly occur together. One study found over 50 percent of the subjects with hypothyroidism also had SIBO compared to just 5 percent of healthy controls.

" You can support optimal gut and thyroid health by eating regularly scheduled meals that are rich in dietary fiber, limiting added sugar, and supporting optimal digestion as needed with digestive enzymes, bile extract, and/or HCl." -- from rootfunctionalmedicine.com
From reading the first one from nih.gov it just seems to say, yes, people who have hypothyroidism are likely to get SIBO.
The second website (kresserinsitute), has much more information, and even at one point says that treating hypothyroidism led to worse SIBO.
FYI- I wouldn't recommend not treating hypothyroidism just to avoid worse SIBO.
To your question, from the research I was able to see from (15 mins) reading/scanning these, it doesn't seem that by treating your hypothyroidism, your SIBO would go away.
Almost all the websites acknowledged a need for antibiotic and probiotic treatment to treat the SIBO.
I've also checked out some reddit posts on SIBO, and in coordination to my own experience, a targeted 2 week treatment of SIBO (antibiotics, low/no sugar diet, plus probiotics) seemed to DRASTICALLY heal/fix/reduce gas symptoms in most people (including myself).
The thing is depending on how bad the situation is, its more about keeping it gas free in terms of being SIBO free.
IE you can get rid of gas quickly with the antibiotics and restrictricted sugars/starches. But if you decide to reconsume food for the bacteria too soon (before repopulating your gut with enough probiotic to overcome/overwhelm and dominate in your gut over the bad bacteria) then you just keep getting gas anyway.. ---That's what it seems from the reddit posts and also, this idea was hinted from my experience too. ---> On my first round of Xifaxan, I actually did need it everyday to reduce, when I forgot a day, the gas did come back (keep in mind, I was low/no sugar and taking probiotics). On my second round (a few months later), I must have repopulated enough that I only needed 2-3 days of Xifaxan and then I just kept the rest of the bottle at home for a gas emergency.