Can you switch from a Tourist Visa to a Non-B Visa while in Thailand?

It depends on your employer and their relationship with the local immigration office. It's a lot more paperwork for the company to do an in-country conversion to non-B so they generally prefer people to go to a neighboring country to get the non-B. But if your company says it's okay, then it should be fine.

Just remember, a company that tells you it's fine to start working while your work permit and/or visa are being processed is lying. You are not allowed to do any work without both already issued to you.

The company has no problem lying because if you're caught, you get in trouble and they don't get punished at all.