I have completed clearing of the rubble. Will pieces of the tablet still come up for my collectables even though all the rubble is cleared?
Also, do I need to have VV3 open for the statue to be completed? I close out and come back and the little guys go and do other things instead even though I left them pushing the statue.

For the first question, yes, the tablet pieces you are missing will still appear but very infrequently.

As for the 2nd question, I am not so sure. I closed my game but left it running and at a certain point, all the builders and chief had wandered off. I put them all back to work and later closed out the game again and when I turned it back on, the project was finished.

It was my experience that the only way to keep the villagers working was to leave my game open. Otherwise they just wandered off.

But with leaving it open, and with the maximum number of builders working on it, I got it done over one night.

I suggest you leave it open. It usually takes way long if you don't.