We normally don't think of a Remington 7600 as a varmint rifle, but the gun has some interesting design features that contribute to accuracy. For example, the barrel is floated by design. My .30-06 is a very accurate firearm, keeping its preferred load inside of 1" at 100 yards. That 1:9 twist will stabilize anything up to about 100 grains. Lighter bullets will be stabilized too, don't worry about that.
Is the Rem 7600 a viable varmint rifle? We normally consider the 7600 to be a big game rifle. Whether you can use it to hunt varmints is directly dependent on your marksmanship ability, your hunting skill and the size of the varmint.
That said, years ago I used to shoot crows with a .54 caliber muzzleloader during the off-season months to stay tuned up for deer season. I don't think anyone would consider the TC Renegade to be a viable varmint rifle, but there are crows who would disagree with you, were they able to find their heads and vote.