The barrels heat up very quick. I say you get 2 MAYBE 3-4 shots before the barrel heats up pretty hot and you have to let it cool for 15-20 minutes. You'll want a rifle with a thicker barrel for precision long range game. I took an elk with my 300wm this past year at 720 and so I know first hand it is a great long range hunting rifle. But I would reach for other rifles to go out to long range shoot for fun before the X bolt.
Yes, the HC could do both. You'll be better off getting two separate rifles for hunting/long range shooting though. However, do whatever the budget will allow. It couldn't hurt to get the HC and use it for hunting and long range and then get a rifle down the line when you can afford/want to get something that is dedicated for the sport. Howa makes a decent rifle that can be upgraded easily. 700s are great and I have had pretty good success with Savage as well.