My brother works as a straight escort, so yes, it is possible.
He has never advertised, and operates entirely by word of mouth. One of his friends with benefits commented to him one day that she had a lot of friends who would pay good money for his services......and so it began ;-)
His demographic is almost entirely East Indian women from 25-45, and female escorts wanting somebody to pamper them and tend to their needs and desires.
He also works as a sexual surrogate, and charges substantially less for that.
I also had a boyfriend who worked as a straight male escort. He did advertise, and was not particularly busy. Perhaps a couple of 4 hour dates a month. He did advertise, and even though his ad was extremely clear about him being straight, he would literally get dozens of calls and emails a day from gay men every day. So I'm not sure how well advertising works for straight males.