Does training 100m speed help in the 400m?

I told my coach I wanted to focus on shorter events 100 so I could improve my raw speed, and then be able to apply it in other events. She had no objection but I lowkey don't trust her opinion as an assistant XC coach running our sprint program. I just want to know if I'm being dumb. I haven't run a 400m or 200m this season, as I'm currently sick and don't want to do long sprints, but i just PRed today with a 12.42. Based on last year's performance I'll probably run around 56 (I already did as a relay split). I've been told I'm better suited for the 400m. At my current times, is training for speed going to benefit my 400m as much as longer lactic training? I want to get really good (as in sub 11, 22, or 50) at something, but im a little cooked cause i'm already a sophomore.