Just like Obito still kept some chakra after the Bijuu were taken from him (he wouldn't have been able to take any bijuu from Madara otherwise), Naruto still has some chakra left in him from all the bijuu except for: Yin Kurama, 8-tails, and the 1-tail.
Obito is giving him some of those chakra now so it's really illogical to think that nothing would happen from that.
Personally, I think that being a jinchuuriki or severe interaction with a Bijuu causes great biological changes in people in NV. That's the reason the Kin-Gin bros kept some of Kurama's chakra, that's the reason Gaara still has some of Shukaku's abilites and chakra even after he died and was revived, and that's the reason Jinchuurikis die after having their Bijuu extracted.