Kaguya hasn't shown any speed that's special, neither have Naruto or Sasuke for that matter. Even if he reacts to them, it won't say much speed wise. At least not against Guy.
If by speed that's special, you mean anything visually impressive that looks like it can be fan-calculated (like distance traveled/time interval) or physics-breaking then no. Although that's a relatively narrow way to quantify speed by flashiness, when there's an obvious power hierarchy that does tell us that Kaguya > full-power Juudara > 8-gates Gai in reactions. And Current Naruto just went about speedblitzing the strongest character in the series, which says A LOT about him speed-wise, as he'd be the fastest character to date. Sasuke himself is at a speed where the same Juudara that Gai nearly kicked admitted to be particularly fast. If Kakashi does indeed react to anyone of them, he certainly would be able to see and counter Gai's speed. Maybe not with his PS precisely, but a mix of dimensional intangibility and instant Kamui would do.
Except none of those three are as fast a Gai.
That's ridiculous. Are you insinuating that Gai is the fastest character in the series, when the second to last chapter showed a character who's significantly faster than him in feat?
Speedblitzing Kaguya >>> Speedblitzing a one-eyed Juudara.