No, I do not think that the View would be the same without Barbara Walters, because the View needs to have some star power in it. Most women do not want to fold laundry while they watch a bunch of women that they do not even know talk about current events. But most women know Barbara Walters, and she is a huge pull for the show.
I think the appealing part of The View is that there are a number of women from different backgrounds and belief systems discussing current issues. This is something that can remain appealing regardless of specifically who is part of the cast. Barbara Walters is often not on the program due to other commitments anyways, and the show does just fine without her.
Yes, it can still be The View without Barbara Walters. Although Barbara Walters is the most famous voice of the show, it is ultimately about a show about women with various opinions taking about a large range of topics. Therefore, as long as the format is the same, it will be The View.
Changing the cast of the View may not change much aside from Barbara Walters. She has such a distinctive personality as well as distinctive and recognizable speech and delivery that removing her would truly alter the show and how it works. The other folks are more interchangeable, but Baba Wawa is unique.