Personally, I think they could have gone on without Spiner, but Stewart was indispensable. He was the captain of the ship, and if you look back at the TV series many of the best episodes were episodes that he had a large role in. Here are a few:
The Inner Light
The Measure of a Man (both Picard AND Data)
All Good Things
While I love TNG and I love the ensemble cast, I feel like the show would have been missing something really important if Picard hadn't been there.