Would the Valar have ever driven Morgoth into the void without the Noldor's rebellion
 

Without the Noldor doing what they did there would have been no Earendil; so there would have been no messenger on behalf of the two kindred; so there would have been no War of the Wrath. Morgoth would still be troubling the world in the 7th age if the Noldor hadn't got a bit naughty when some glittery things got nicked. :Merisu:

If he didn't succeed with the Noldor, Morgoth would have found some other people to corrupt, and there would have been a different Earendil and a different War. Or, alternatively, he would not have succeeded with anyone, but the Valar would have guessed his intentions and kicked him out before he got out of hand again.

However, his plans worked on the Noldor, so everything that's above is just "what ifs". The Noldor were such a people that Morgoth could not have failed to rile them up.

The Valar would definitely have kicked Morgoth out...after half the Elvish population in Beleriand was wiped out. Then they'd cup their chins in their hands and say, "Hmm. Enough talk. Let's do something."