Can you access discord from the standard web? Are people likely to land on the place from a standard search? Do people think to search such things within itself? Is the service likely to be around/popular in a few years (it is a proprietary chat protocol you can't run your own servers for... history gives many fine examples of such things failing)?
So that is no, no, possibly but unlikely, and no if history is anything to go by (teamspeak, ventrillo, mumble, google talk, yahoo, AIM, MSN... this could go on for a while).
To that end why would you do that over a standard website? If you want to have it as a backup or chat for your website... I would suggest somewhere you could have some guests more easily but your time to waste.