ICF 5X5 without Bench or OHP? (waiting for strain to heal)

[BBLurker4Life]

Hey everyone, I know I've made some threads about this already, but I think this one might be the most important. I got a pec strain about a month ago doing pushups in some crossfit circuit training thing (not a crossfitter but was doing it for fun with my friend). Anyway it hurt a LOT under my armpit and I could barely do normal activities that involved my chest without a lot of pain. Now, I'm a lot better but I just came back from my first ICF session and something didn't seem quite right. I REALLY don't want to go through the whole recovery process again so I decided to not work chest or do pushing movements like OHP for at least 3 weeks while still doing every other exercise just to make sure my chest is brand new before I try to add weight to my bench. I don't want my chest to be lagging though so I just decided to cut on a small deficit and just do the program's cutting version until my chest feels 100% again. The only thing I'm wondering is: will doing this still train my CNS for the program so that I'll make gains when I start bulking again? Or will I have to wait the 1 month period because I was cutting the whole time? Answers would be awesome cuz I'm kinda bummed about the whole thing. Thanks brahs.

[BBLurker4Life]

Chest bump. Haha puns.