Technically I don't think you're allowed to, but some people have been lucky. I was actually in a Bangkok Bank branch when a guy came in and the bank manager told him that they don't open accounts for tourist visas.

Based on my experience, I think they've made their decision up before you even arrive based on your paperwork.

My girlfriend has had the same office job for 11 years in an investment frim and has multiple pieces of rental property and she was still denied with them asking only two questions.

I thought how ridiculous is this that you can't apply and receive a proper tourist visa but so many people come across the border illegally and are given benefits.