This is one of those 'ask ten different people and you'll get ten different answers' type questions. There are a lot of those in Thailand trust me.
Although the official line is 'no you can't get a work permit without a degree' there are plenty of examples of agencies managing to get one for their teaching staff and in some cases, teachers at government schools out in the sticks have had no problem at all.
As in most cases, it can depend on contacts and being in the right place at the right time. If you're looking for some hard, fast rule that applies 100% of the time - forget it. This is Thailand.