There are options for persistent connections, with logs and detachment, etc. ZNC/PsyBNC/Quassel come to mind. ZNC, in particular, is extendable via Perl or Python (or TCL if you're a masochist). I hear good things about Quassel as well, but it's still early in development.

I get Android notifications if I'm detached from irssi in tmux and someone PMs, says my handle, or any number of custom triggers I set. All free & open source (other than the android phone).