I don't think the fox would be able to control it, well there is at least the possibility that it can't.
Also, can the fox gather anything external at all? It is SEALED after all. It might only have access to it's own energy.
If it could gather Sage Chakra, do you not think it would have done that in the past (when it was DESPERATE to be set free) and just give Naruto the chakra, causing him to mutate and die.
There is a risk the fox would die also, but I'm pretty sure it would either be relseased or regenerate at a later time.
Anyway, the point was, Sage Chakra (if it was capable of gathering it) would have been a fantastic method of escaping Naruto. Even although only some chakra was deliberately leaked into Naruto's body, even a tiny amount of Sage Chakra (before Naruto mastered it) would have been enough to ruin him...