Can you go on holiday outside Thailand while waiting for a marriage extension application to be processed?

Twice, funerals have necessitated my return to my home country (UK) during this month after applying for a year visa marriage extension, and there has been no problem whatsoever.

On one occasion, the lady at immigration (Jomtien) even assisted by extending the period to six weeks, instead of four.

I did it in the past with a re-entry permit.

You can if you get a re-entry permit, but better not. During that under-consideration period, IO would contact you for visiting your house or witness interviews (depends on immigration offices). If you have a plan to travel abroad already, don't forget to talk about your schedule out of the country with IO when you apply for your next 1-year extension. But be ready to be told 'stay'.