No, the 57 Ford is a totally different chassis. You could use the AMT 56 Thunderbird chassis or even the AMT 56 Ford but that one would not have the center "X" member.
Also, with some surgery you could remove the front bumper from the grill on the 57, trim the bumper to clear the fenders and use the '56 Thunderbird grill, same grill. Now I never checked scale accuracies but the front clip from the 56 can be swapped and use the 57 bumper.
As seen by the comparison pics, the parking light holes are the only difference in the front clip. Gray car is a 57, red is a 56