@eludom AFAIK there is no gateway from clearnet into Yggdrasil. However, #Yggdrasil appears as just another interface on the box - tun0 by default. A public webserver that listens on port 80 would be instantly accessible both places. There is something of a convention of prepending "y." before a domain name for an Yggdrasil in-net version.
In the other direction, at least one person operates a public proxy from Yggdrasil out. And of course, the entire thing can run atop current Internet.