Can I travel outside Thailand and re-enter with a Non-B visa and work permit?

Make it at the Immigration office the 1st time, only to go safe.

You can get a single re-entry permit at the airport (or go to any immigration office before hand). Give yourself a bit more time to do it, and explain to immigration that you want to get it before going to the departure lounge. 1000baht.. a couple of photos (?) copies of passport, visa and maybe the work permit. I forget the exact documents, but you can find out on the Thai immigration website. Fill in the form and hand over 1000baht for a single re-entry (i seem to remember you will be asked the exact return date...be aware of the day time u expect to get to the immigration desk when u return.. especially if landing just before midnight). If you will do it many times with-in one visa, get a multiple.

@Skylar ***********

you first need to understand a work permit does NOTHING as far as letting you stay here (which you do with the visa and extension) OR let you leave and come back (which you do with a re-entry permit) 🙂

You need a re-entry permit separately from your extension to keep your current stamp valid. A re-entry permit is single entry (1,000thb) or multiple entry (3,800thb).