Will this shower trim work with my existing setup?
Unlikely. 

The new one has a square ferrule, yours is circular (hexagonal?).

You would need to get the escutcheon cylinder off of the new one and it would have to fit the old (or reuse).

If I had to guess, the new one pivots and rotates, where as yours just rotates. The action on the new lever seems to me like it would be un-ergonomic, if so.

Swapping out just the cartage might work, but I've no idea how to do that even if it's possible (and you'd be one lucky sob if you found them easily interchangeable). I've never tried to repair one with non OEM parts.

I also see no means of attaching the new escutcheon plate. Caulk is supposed to hold it, eh? More things I don't like: square handles and plastic ferrules. Whatever you do, Do Not discard your old parts, or you might be sorry.