It does, unless the speed difference isn't massive.
Amped Momoshiki had a massive speed upgrade seeing as he blitzed the Gokage. Up to that point, they kept up with him and Kishinki.
Naruto was able to react to him, which implies his speed was relatively close to Momoshiki. Comparatively, war arc Naruto at Base would have gotten fodderized if he had fought amped Momoshiki, implying his Base while at adult grew in speed since he was slower at that level earlier. The point finally is this; Naruto doesn't necessarily need to train at Base. As I said earlier, it's likely his Base strength increases as a side-effect of using Kurama chakra.
Speed is relative to the stituation. Is naruto foot speed in base form faster than sasukes? No is it as fast or faster than momo? No. you can do battle with an opponent far faster than you but it won't mean you have equal speed than them. Naruto was getting tagged so he needed the kyuubi mode to put it on equal grounds