Plugging and unplugging a serial cable is equivalent to plugging and unplugging an ethernet cable. You're not removing or connecting a device, only what the device connects to. So plug-and-play has nothing to do with any of it.

Are you saying that your computer works fine unless you have a serial cable attached to it on bootup? That's weird. Just leave the cable off until you've started the OS, then plug the cable in. You'll be fine. People have done it that way for decades.