I am curious whether some educational institutions in Thailand offer "continuing education" to Thai's to allow those that may have had to drop out of the education before completing there high/secondary school .... to go back and get an high/secondary school equivalency diploma?

I believe it is possible and that it could be done by correspondence if you were living overseas but you had to come back to take some sort of exam to get the High School certificate. This was certainly the case a few years ago. Probably changed by now. I can't remember who exactly was offering this I'll try and find out.

Yes, it is possible to continue your education as an adult (non-formal education). Even in small amphurs this is possible. But I'm not sure about the details and the degree. But adult education is very popular as far as I can tell and often done in the weekends. in the bigger towns it might also be in the evening.