It's hard to say...

We had a 3 legged doe running around last year which got around very well, and had obviously gotten used to it's loss of a leg. From what others said ( I had not seen it ) it appeared to be an older deer, and when all the does ran, she would keep up. The wound was also said to be old..

The biggest problem comes in the winter, if it isn't clever, it will have a hard time getting food without being able to scrape the snow away with the front leg.

It also depends on the severety of the wound. It could heal too...