Which Varmint barrel do you have? If it is the 243 or the 223 then yes, they are thicker than the normal handi barrels in the same calibers. Shouldn't be a problem interchanging between the two different kinds of stocks though as long as you are using one of the barrel float tricks listed here. You may have to relieve some of the plastic from the foreend of the syn set with some 80 grid sandpaper but I'd try it first before I did that.
I take it you have the 44 mag scoped or else you wouldn't be wanting a monte carlo stock. I suggest, and I know MSPR will agree, that you go ahead and and try the standard stock synthetic even if you do have it scoped. I thought I was just going to HAVE to have a monte stock for my Huntsman after I scoped it, but after shooting it I have found that was false. In fact I hardly could tell the difference. However if you are intending to use the iron sights on the 44 then the monte carlo stock will be a pain in the neck......literally, you won't be able to find the iron sights while using the monte stock.