I have broken more HDMI cables than I can count. The things are fragile. Please do run at least a conduit that is big enough to pull a replacement cable through.
Probably does not matter if you put your existing cable through the conduit or not but if you add a thin flexible wire or cord that is for pulling a new cable in you might want to make it double length and tie off the ends so it does not get lost and make sure all your bends are gradual so the connector can get through easily.
Might also want to avoid any right-angle connectors unless you can access the removable cover plate that is oriented at the 45 degree or you may have issues pulling a connector through.