Can't hurt to try!
Or you could even not mix the pudding and whipped cream together, and just layer it.
If you're going to mix it in, use the "folding" technique, rather than just stirring/mixing it in. Be gentle with the whipped cream!
And for the record, real whipped cream freezes in an incredible fashion. My mom used to make a hot fudge sundae pie, where you take a crushed chocolate wafer crust, then layered ice cream with homemade hot fudge sauce, freeze it, another layer, feeze it, another layer, freeze it...then top with scads of whipped cream and freeze that, and it's INCREDIBLE. I love things like that.
Good for you for trying to make it healthier with real foods! Next step? Making the pudding from scratch! (hardly more work than cooked (not instant) pudding, FYI)
(says Molly who started making Paula Deen's "is it really better than s-e-x" cake as the recipe states, with boxed mix and boxed pudding, and is now making it with from-scratch yellow cake, from-scratch pudding, and organic heavy cream whipped, and nearly gets marriage proposals (I used to just get compliments on the original version) from all of hubby's co-workers who try it.

)