A deep and interesting question. Somewhat contrary to you, I beforehand tended to reflexively say "yes" (maybe due to me being a physicist). But upon rethinking I now think that there's a straightforward counterargument.
The very notion of a law entails a restriction, namely that from a (maybe infinite) set of possibilities that are there without that law, to a smaller (but maybe still infinite) set of possibilities in agreement with the law. A law that doesn't impose any restriction on anything, simply isn't a law. I think this holds in generality. But let's turn to physical laws. A physical law is, in the broadest sense, a restriction on the set of possible states of a physical object to be in. The Maxwell equations, for example, rule out for the electric field to propagate totally independent from the magnetic field. Both fields dynamically depend on each other in a lawful way. If the Maxwell equations would not hold, then there would be a lot more freedom for electric and magnetic fields to evolve. But let's proceed: the Maxwell equations still leave open the possibilitiy of there being such thing as the ether as their medium of propagation. However, nobody found any evidence for the existence of an ether, and Einstein finally put an end to it by introducing his special theory of relativity which is not consistent with the existence of an ether any more. That is, his theory is more restrictive (and also contradictory to old-school Newtonian mechanics, for that matter). Since then, there has been plenty of evidence in favor of that new theory, so the scientific community had to abandon the ether as a possibly existing thing in this world. But the existence of the ether is still logically possible (that is, by denial of the theory of relativity). Thus, as we have empirically found that Einstein's theory is correct (so far), we have to exclude the physical possibility of the ether in this world. There are, however, infinitely many logically possible worlds where Einstein's theory does not hold, and in some of these worlds there is an ether. In our world, there is no ether, but the set of possible worlds consistent with there being no ether is, of course, still infinite. In fact, the set of physically possible worlds consistent with all our most modern theories is still infinite, to the grief of physicists hoping for the "theory of everything".
Concluding, the set of logically possible worlds is (by far) not equal to the set of physically possible worlds, if by "physically possible worlds" we mean those worlds that are consistent with physical laws, including all their variations (like different values for the elementary constants and such). Progress in physics is finding stronger restrictions on the set of logically possible worlds. If you took away all physical laws, then the set of "physically" possible worlds would become equal to the set of logically possible worlds, but then this wouldn't mean a lot any more.