Why are you nitpicking. Read the next sentence.NO. I do not agree with that. If you give another ninja chakra and he do not performance healing jutsu on himself, his wounds will not heal faster.
Now if that user does performance healing jutsu on himself after getting chakra from somebody else, his wounds will heal faster.
By "heal" I mean natural healing of the woulds without using any healing jutsu. Natural healing is something every human has. White blood cells heal your wounds.
When do you think your wounds will heal faster,
1) when running out of chakra and exhausted or,
2) when your chakra is fully restored and you don't feel exhausted?