Yes. HD 5770 will suffice as long as you do not expect it so run every single game at high or max graphics quality.
You got your desktop for that right?
I have a 9600GT in my HTPC. I haven't really used it to play games. Mostly to watch videos on my HDTV. The most GPU demanding game I played was Fallout 3, the most demanding CPU game was X3: Reunion.
Even on my main PC i dont run maxed out due to temperature.... I really dont like to get my cards above 60C cause then i start to sweat. I keep the door closed cause the stupid AC controller for the house is right outside the room.
Majority of the games i would play on my HTPC are probably single player RPG's and other things the wifey could get into. We played Monkey Island for the Wii, but the graphics were terrible! I already have a PS3 for blu-rays.
Anyway, what if i were to SLI something considering thats my mobo's capability. I am all about quality product. So if i were to find a good 5770 i would probably stick with it.
MSI R5770 Hawk Radeon HD 5770
*edit* and what is this display port people speak of?