I have a DAVS-880 which is the big brother of the 550. I think the inputs are the same at the back and if this is the case then you can play your PS2 thru it.
The video 1 input will take phono and video jacks so you can receive a stereo signal. If this is a Pro-Logic signal then you will have to tell the system to interpret it as such. The better solution is to utilise the standard video input and optical audio input for Video 1 and connect it to the optical output of the PS2. The system will then decode the signal for you and will even allow you to play Dolby Digital games (GTA-Vice City is one).
The Video 2 input will take standard phono plugs so you could output your tv through those. I did for a while, but got too bored with having to select Video 2 every time I wanted to watch tv and then having to juggle the volumes on the system and the amp.
Of course if the inputs on the 550 differ from the 880, then none of this applies!
FWIW the newer Sony DAVS systems have RGB output which is, I believe, better than the S-video output of the 550/880. I'd have a look at those. That said, I prefer the look of the older DAVS systems.