I can guarantee you that Apple and Google can serve out app downloads that max out a 10Mbps, or 100Mbps connection with no issue. For some large apps that are several hundred megs, to a few gigs, that would make a huge difference. For your average 10-25MB app, the difference would be negligible.
I agree, having the faster speed will make a noticeable difference. If it didn't then why would carriers spends millions to upgrade their network to LTE Advanced, etc. The servers that serve the apps\content can without a doubt saturate the connection, I have downloaded files at 330Mb/s from Apple, YouTube, Netflix, etc. from my home connection. My Cellphone Carrier also has fast speeds, and can download things extremely fast, which makes a noticeable difference.