It could go either way with him.
Kaguya did deny it, and Aka said in a volume extra that he accepted it at the time, but there's been hints that he may have figured it out after he got over his fear. Such as leaving them alone together during stargazing before Kaguya even came up with a plan, only to watch and take a picture of the most romantic moment.
Even when they were shopping for Christmas gifts, his guess (which Kaguya confirmed) was that it was a boy she likes at Fujiwara's Student Council Christmas party. It's not exactly hard to figure it out from that, so he's probably just letting Kaguya wait until she's ready to say who it is.