connecting to a low rez monoitor will increase picture fidelity but it wont fix poor gfx from the gpu. ps2 uses the pal/ntsc standard so 520p max so no hdtv outputs at all. (the tv will upscale the image but will blur it while doing do)
if you can find 1 grab an old 800/600 crt monitor that has a y-sync input, and the image will be pin sharp.