You can try, last I remembered it doesn't hurt the modem but if it doesn't have the filter installed in that line then it won't connect.

There's not much practical benefit to a hardwired cable modem versus a decent wifi setup.

I would probably run an ethernet cable through the crawl space or attic or such if I really wanted to do that and then leave the cable modem where it was and install a switch on the other end in the bedroom.

If it's a Wi-Fi cable modem then it's kind of like better off centrally located or right next to the centrally located Wi-Fi router.