I left and got mine, but NOT to Thailand. They can ask for proof of location, but possibly not likely if you provided adequate proof originally. However, I wouldn't recommend going to Thailand during the application.
I had successful applications after travelling, but sent letter making it clear no travel to Thailand and returned to country of application. They can come back asking for proof of location - they did in my case, hence I went back.
It's not true that you can't generally travel during visa applications, many countries allow this. It's not clear though whether it's generally permissable for Thailand. Also different embassies may treat differently. But I was successful after making it clear that I had.