FATTTTDADDY
Congrats on a super deal! I purchased a Ruger M77 with a Leupold M8 4x mounted for $400 and I though I got a steal!
You ask if they shoot the answer is a qualified Yes. I have two M77s and two M77 MKIIs and they all shoot. You might want to do some tuning up, however.
First thing I would do is float the barrel, then reseal it with polyurethane. This job takes about 10 minutes with a Magic Marker, sandpaper and a screwdriver. After removing the stock, loop the sandpaper around the Magic Marker and sand the barrel channel so that it doesnt touch the barrel when the action is installed in the stock. I use a $1 bill to check for clearance. While your new rifle may shoot great without floating, I float all my barrels. When I got my first centerfire (one of the M77s) I discovered I couldnt zero it the more I shot the more the bullets walked up and to the left. Floating the barrel solved this problem and prevented others.
The second thing I would do is tune up the trigger, another job I do to all my firearms. Some Ruger triggers are excessively heavy, others are pretty good.
Heres how my Rugers can shoot when things go right (wind, etc.):
M77 7mm Mag = 0.266, 3 shots, 100 yards
M77 .257 Roberts = 0.65, 3 shots, 100 yards
M77 MKII .300 Win Mag synthetic (canoe paddle stock) = 0.85, 4 shots, 100 yards
M77 MKII VT .22-250 = 0.50, 4 shots, 200 yards