I think its still early going, so it remains to be seen how it will work out. Four Constellations per year would be a good production amount and as you said would allow them to spare the destroyers from being overworked.
Depending on how things play out, the USN could be producing a good number of ships per year near the end of the decade. I think the best possible output case for them would look something like this:
- 4 Frigates per year
- 4 Destroyers (Arliegh Burke or whatever the successor is) per year
- 3 Virginia SSN (2 without AUKUS) per year
- 1 Columbia SSBN per year
So that is about ~120,174 tons of ships per year (destroyer weight is calculated based on Arleigh Burk Blk. 3). As I said above, that is likely the best possible outcome for the USN. So maybe you only get two destroyers a year instead of four. On top of that, you have to have the budget to pay for all of that shipbuilding and that amount of ships would be extremely expensive.