Don't you mean "time off from pitching"?
There's a big difference. One can take time off from pitching, yes---but not from throwing. Many pitching coaches, past and present, say that one needs to keep throwing, as in playing catch, because that's how one maintains arm strength and flexibility. Twenty to thirty minutes a day, you can get a good catcher, have him set up behind the plate, and play catch for that time---or, if you can't find a catcher, mark off a strike zone on a wall and throw to that. But it's important to keep throwing.
Let's look at this way. A baby has to crawl before it can walk, and walk before it can run. A kid has to throw---and I really mean throw the bleep out of the ball---before he can even think about pitching. Now you say your kid has started pitching in Little League---all the more reason to keep throwing, so as not to lose what has been gained. So throw---and throw with intent---throw the bleep out of the ball, and then as spring approaches you can see about the pitching part of it. Good mechanics and balance are, of course, important. 8)