Following Rabenu Yitschak in Tosfot BB 66b (also reported in Tur YD 201). Yes, following Rashbam, Rabenu Tam, RShBA baal hatosfot. The Tur Siman 201 refered to two jopinions and stated that the problem for Kulo Shauv is deorayta. Bet Yosef in the same siman reported that Rambam, Ramban, Rashba and Ran agree with RY. Raavad. There are several kinds of Shauv but the OP is for a Bathtub which is filled normally. In (Shulchan Aruch 196, 53; the Shach said this in his name by dyuk) he ruled as Rambam, this psul is derabanan, the RMA (196, 3) stated as Rashbam and Rabenu Tam, this is deorayta.
A second problem is that the bathtub is already a keli before that they cemented it over the ground. But a bathtub is a keli which is made only to be cemented over the ground.
The size of the Mikve is greater than the size of a standard bathtub but there is big bathtub.
It is not sure at all that biblically a bathtub is a good mikve.
In conclusion, from the Shauv point of view Machloket Rishonim and Machloket Acharonim.