Can I fly to a nearby country and back in one day for my education visa while avoiding issues at immigration?

Check with your school first as if they've already applied to the ministry of education, you may reset the entire process by leaving the country since they would have send your entry stamp into Thailand as part of your application and by you leaving and returning you would have a new entry stamp and possibly void the application your school sent to the ministry.

Otherwise, you can leave and return the same day if you're from an visa exempt eligible country. Whether or not you are allowed in is at the discretion of the immigration officer and will be based on your history in Thailand. If you have an extensive history (multiple months in Thailand already without a long term visa) or multiple entries in a short period of time, you may encounter issues trying to leave and return.