Does Apple TV support a 1600x1200 resolution via HDMI/DVI?
I'm thinking about using Apple TV with a bigger 4:3-TFT with a 1600x1200 resolution. Does Apple TV support this?
Not officially no.
How would you be connecting? HDMI or DVI?
Might or might not work - AppleTV 3 officially supports 720p and 1080p but depending on the negotiation with the TV/monitor other modes may show up.