Still takes time, energy to make ice cream, then store it along the way.
Why not just use milk, flour, eggs, sugar? And then you control the proportions.
Store bought ice cream, you have no idea the proportions, then there’s over-run (how much air is trapped in the ice cream) making volume different, and unless you get a “natural” ice cream, there are thickeners like careegenan. Who knows how that will affect a bake.
This is a bad solution in search of a non-existent problem, with wildly unpredictable results. Everything in this recipe can be found in dry (powdered) or canned form, which would produce far more consistent and better results.
I keep both a powdered and canned milk, either which I could serve to someone and they’d have no idea. Egg crystals too.
Baking is already a very picky chemistry problem, adding in crazy variables like will just result in poor results.