In both cases its going to depend on how much organic material you can get into the soil. If you want to aerate and top dress a heavy clay with compost then you'll start to see improvements relatively soon and adding OM to sandy soil will improve its water retention almost immediately

It was probably a year until I noticed much of a soil difference, but the plants noticed something changed within about two months. They were growing much larger and healthier very quickly.

Coming up on two years in, the soil changes are obvious and continuing, but I think the plants don't see much further change (or, additional change doesn't matter so much). They're still large and healthy.