Oh, absolutely! As long as you keep the iPods under the same iTunes account as the iPad, you can transfer any iPod app over ... easily. In fact, IMNSHO, it's much easier
TO keep the account the same, so you can transfer without having to rebuy them.
I have to admit, however, that I got a chuckle over your auto-corrected post. Rebuke those apps!

Sorry - but that was cute 'cause I had a mental picture of you shaking your finger at those apps - making sure they behaved while on your kids' iPods.
Yeah, I'm weird like that....
But, seriously, I hope this helps/reassures you about the transfer.
Marilyn