Yes. But I think it's getting harder to pass unsigned code.
Take the original xbox, for example. First, a modchip was required to pass unsigned code below the radar. Then, exploits using game hacks came along and made the process easier.
Now for the psp. The psp version 1.0 and 1.5 are a homebrewer's dream. I've done a bit of homebrew gaming on it, and its quite good. But with each new patch on the psp, sony changes things around, tightens security, etc etc, to the point where psp hackers are always a version or two, or three, behind in hacking progress.
Now for the xbox 360. Microsoft got wise this time, and made it a real doozy to develop mod chips for. That is, they surrounded the bios in epoxy. Also, if code does manage to slip by, and microsoft catches wind of it, they will most likely fix the problem quickly (as I see it, microsoft wants their xbox live service to be unblemished, unlike their other products/services) through automatic xbox live updates. And, say, if you arent hooked up through xbox live, how in the world would you sucessfuly spread the virus to other consoles across the world?
PS3 will most likely carry the same tight security that they have with the PSP. I imagine the PS3 hacker community will be pulling their hair out when trying to work with the already difficult-to-develop-for PS3.