My $.02:
With a proper bullet, appropriate scope, known velocity and ballistic coefficients, and either a good ballistics program or a lot of range time, I think it's a viable proposition to stretch out the 444's range. If you account for the substantial drop involved, I bet those big .429", 265 to 300 grain bullets will kill deer at ranges far beyond what you'd expect.
A big drawback I can see is the gun itself. While my experience with lever actions is quite limited, I can't see them being all that accurate. While this isn't an issue at the close ranges at which most 444 users shoot, it could quickly become an issue at longer ranges. You would also have to contend with the usual issues facing long-range shooters, namely the rapid bullet drop and potential for wind drift.
In conclusion, is a 444 with a ballistic compensating scope a viable hunting weapon? Certainly. However, I feel you would be better served with a bolt-action rifle in a standard cartridge if you think you'll have to shoot at ranges beyond what a 444 is normally used for, even if you are just as likely to hunt in timber where shots may not exceed 50 yards. If you're set on a 444 Marlin, I highly recommend a 4x fixed or 2-7x variable scope.