No, not under original intent. See Barron v Baltimore (1833). The 5th Amendment did not apply to the states, and then only limited, until 1898.
I'm no constitutional scholar, but I remember reading somewhere where the 1a was used against a southern state jailing baptist ministers in the early republic. I'm sorry for not being able to cite sources, but if true, it would mean the fed. bor would trump the states, which should be the case, IMHO.