Then if it's bloodthirsty players who have odd ways of playing, your idea has a good and bad part.
The good part being that if they're somewhat crazy, that makes for a good back story and good roleplaying. Maybe they, like most homeless, are psychologically unstable. making many of their choices illogical and odd (which could throw off pursuers!). I brought up the 'chasers' are like a party of players because they can not only see what it's like when a group of psychotic players chase their prey, but they could get a feel for how their actions affect the mindset of NPC's (maybe I'm getting too into this psychologically...). Also, for a future adventure after this, you can bring up a quest/adventure of the players chasing their old hobo characters! They'll never see it coming mwahahahaha...
But a bad point I see is that they may be use to overpowered weapons, and the lack of may cause headaches. Perhaps they witnessed a murder of, lets say the mayor of whatever city. The murderer set it up to frame someone, but the setting they did it is a setting the players can get into easily, thus finding the scene first, and maybe taking the weapon of said killing (which was supposed to be used as evidence against the intended target.).
This could then make 2 groups of people who are after the players, the police and the mysterious murderers.
just thought, I like the idea btw. Im just typing what comes into my head as I type, so I may ramble a bit.