Yes and no. A synthesizable design, aka soft core can be ported relatively easy between different processes.  You can think of it as the source code of the chip which has to be compiled for a process.

But thats not the problem; what we call a process, consists of pre-made transistor designs and a whole set of design rules. Thats different for every process, and almost every fab. So you once you "compile" your design and generate a mask, its no longer portable and you will still need a specific mask for every process.

Since the cost of that mask is what is preventing ASICs from being available today, I dont really see what problem open sourcing a design would solve. It might be neat project for a hardware engineer, but who's going to pay the mask? And why wouldnt he use a less portable, but better optimized design? A soft core is never very optimized.