No, routers usually use a stripped down version of linux, so there is little chance the correct drivers (kernel module) exists.
And, how would OpenHAB connect with the device? Only if OpenHAB itself would run on the router.
Network devices that share USB devices do exist, so you get USB over IP.But it’s quite pricy and you will still need to run OpenHAB somewhere.
As it is a serial port you may have some luck sharing the serial port over the network.
You would run than something like a comm port sharing utility (e.g. socat) on both sides.
That way you can put the zwave stick in a router at a convenient location and the server in another.