Um, no its not, not in this day and age. Tramp is also used to refer to prostitutes, permisquous women, sluts and *****s, and porn stars. I'm sure you've heard a woman refered to on tv or a movie as 'tramp' at least once in your life.
I think you need to update your definition of the word and understand the difference between vulgar slang and literal meaning Norm.
Its ironic, since I wouldn't personally refer to the homeless as tramps anyway, but rather the indestitute or disinfranchized. Ultimately, I don't refer to them any differently than I would another person who is otherwise fianancially stable. I don't 'call' them anything, I imagine most people don't. I treat them the same way, but realize they need help.
"Hey you, tramp, heres five dollars!" Doesn't sound right anymore if you're talking to a homeless man or woman.
Finally, I see a tramp as a drifter, someone who hustles people on the streets to make it by, someone who makes SOME money, but travels from place to place to avoid being arrested. While it could be called the same thing as what homeless people do, the word 'tramp' could imply a different situation alltogether.
Anyways....back to the show. 😛