Is the set defined by this inequality convex or not?

Please re-read this link which has previously been provided to you.

abs(y) on the RHS of <= makes this non-convex. That is, of course, unless c <= 0, in which case the constraint reduces to x'*A == -b, y == 0.

Whether there is a convex modification of this constraint which makes sense for your intended use is up to you to determine.