Does it make a difference if i do or do not send my injured player for rehabilitation in the game?

Yep.

If you don't, then that injury will occur in the future and it could get worse...

If you do he's gone with his injury for a longer time. But I'd never risk not letting a player go on rehabilitation.

Also if he is going to be out for a long time, (6 months or more) then if you send him to rehab he may also come back earlier then expected. When i was manager of everton, i sent Duncan Ferguson to rehab because he had a damaged spine and out for 6 months. And to my delight he came back fully fit within three!!! (well in some ways, fergusons s**t, but i needed the backup)

Thanks for the input. :)