No. I've looked on the Savage website and the none of the wood-stocked Mk IIs have a Picatinny Rail. I didn't look at the composite stocks.

Unless you buy a rail and bolt it to the forearm of your rifle, the first bipod won't mount on your rifle, either. There would likely be little advantage buying a rail and doing this. By the time you finish, you could've bought a decent Harris bipod which doesn't require the rail, just a swivel stud.