They can deny you... Always. The question is, will they deny you?
I have been here 10 years, most of that time I have been on tourist visas... I could be lucky but I think it's more about Thai Immigration being pretty easy-going.
I think the options are a Visa or the minimum requirements for visa exempt. The requires would be something like proof of more than 20,000 baht, hotel stay, onward travel. You should already have to the first two and onward travel can be satisfied with a bus ticket.