Hi Noob, welcome to RetouchPRO
(that username us going to look a bit queer after you've raked up a couple of thousand posts!)
Besides being possible it is actually a
very good idea.
Instead of trying to get a low-quality photo to "look good" it is more more rewarding to turn this into good Art.
However...
If you start with a "good" photo, the Art part is usually acheived by simplifying the image.
If you start with a "bad" photo then you've got to put more in (and not take out)
So you will have to word a bit harder.
Hope that made sense,
Rô