You will certainly be able to move a lot of snow in a straight line. What does it have in it for lockers?
The biggest problems that I can see you having are starting on a side slope and turning. The times when you are plowing, it is usually slick enough that I doubt you will destroy axles shafts. Starting on a side slope, if you accidently start spinning, you will be going sideways down the hill very fast much worse than if the diffs were open or limited slip. The locked rear is going to make it so that once you are moving, the truck really will only want to go straight. Maybe with a front locker, you will be able to pull the front around. I don't have any experience plowing with a locked up front, only rear.
My old truck was locked at both ends but didn't have a plow. It wasn't very good for driving around when the roads were only slick but it dominated once the snow got real deep. Basically, because of being locked it was always skidding which isn't a big deal once there is a lot of snow but is real annoying when there isn't much snow.
Who knows, maybe we won't even get snow this year the way the weather seems to be going.