Its a bit of a trade-off, since usually you can build a better new ship in a somewhat-longer timeframe than it costs to refit the engines of older ships, which is why it was always a contentious fact. Most refits were done due to the Washington Naval Treaty, but a few major refits were considered outside of it (the USSR refitted its Marat-class dreadnoughts with new engines outside the treaty, and the USA considered comparable refits such as lengthening the deck of the USS Ranger, and several Pearl Harbor survivors also had extensive refits--not the engines, however).
Refitting the engines, as mentioned above, can give your capital ships a lot of utility for carrier escort; however, in the same scenario with the Italian navy, I'd rather convert the older BBs into aircraft carriers (for whatever reason, the 1922 engine still pushes them up to 30 knots) and just build new battleships or battlecruisers; this also means you don't need to bother with 1936 carrier tech for a while longer, plus Italy starts with the Littorio-class queued at 20% progress (which is going to take a while, but 2 carriers and 4 battleships is a reasonable strike force for 1936 tech).
