Generally speaking, no. Longer time controls tend to help you improve at long and shorter time controls, but the inverse is not true. I will say occasional speed chess can be useful if done the right way, but most don't use it that way - playing a ton of games fast will just condition your mind to move quickly and this is a massive weakness to your chess if you can't slow down under longer time control.
In my opinion, I find speed chess like blitz to be less harmful at higher ratings. Blitz can be good for volume of games and reinforcing patterns, but many patterns are likely unfamiliar to even average chess players, so they need the "extra thinking time."
Just my opinion as of now though; I'm not super set on it, I might alter my view slightly if presented with evidence, but as stands speed chess does not seem to help OTB rating at all - and in many cases, it can actually hurt it if the speed chess is your default.
Can playing lots of online blitz improve your OTB rating??