Do activated hoppers produce less lag than unactivated hoppers?

I know that putting blocks with containers above hoppers can reduce the calculations that the game needs to run, improving the performance of the game.

Does activating hoppers with a Redstone signal (thus locking them) achieve a simillar effect?

Yes, they do. Here is the performance graph after I put a redstone block under each hopper using /fill:

The bottom right graph shows how many milliseconds each server tick takes, with longer lines being more time. You can clearly see the drop when I deactivated all 32761 hoppers.

In this test all hoppers were facing down, I deactivated them with redstone blocks below and I used a render distance of 32.