Can someone on Disability hold public office?

Absolutely. Some are very part time. I bet Tammy Duckworth gets it and deserves it.

technically, yes, but it could be a red flag for fraud....in most cases if you can do that you can work..

no way is He!! does Tammy Duckworth get SSDI.  she is clearly able to work.  Her base salary is $174,000 which is well over SGA.  She is a US senator.  she had other positions before that (and after becoming disabled) that were good pay....she has her PhD.

only exception would be very small town where it is very limited work.  I live in a 'small town' but  they put in a lot of hours...some weeks it will be 20+, some weeks it will be a few...

you are mistaken to think it is 'not  many hours'  I wouldn't be surprised if it was less than 10 hours per week even in a small town....you have people calling/emailing with issues, meetings, public appearances, etc....not to mention campaigning is a lot of work.  the work value is probably at least $25/hour which would get you pretty close to SGA.

if the disability is something like blind or quadriplegia where you can work, but there are no job opportunities that would be credible..While deaf people seem to get benefits easy, there is no reason an otherwise able bodied deaf person can't work...things like stocking shelves and being an overnight janitor don't require hearing...and the deaf can strive for better jobs

Sure. There are Senators and Congresspersons who are disabled.