No, they will not. The Speck-designed Osmo iPad protective cases will only work with the newly designed Osmo iPad base.
How do you know which iPad base you have? See attached images for:
(A) classic iPad base (does not work with Speck cases)
(B) newly designed iPad base (works with Speck cases)
Here's more information about the differences between the classic and the new Osmo iPad bases.