What you're requesting is actually the normal way most of the people I talk to use IRC. I have a highlight buffer[0] script which keeps a history of all the times I get mentioned, and weechat supports libnotify so if your desktop is able to get pop-ups then you will be notified on highlight. (I use dunst for this).
There are also Quake-like terminal emulators that drop down on hotkey- these are also quite common and can make it really easy to just check what's going on when you have a spare second.
I will write a blog post about how to achieve my setup for linux users since there seems to have been mild interest. And I'll do some work on packaging it up so it's easy to take the bits that people like. I am using a fair number of plugins though.
this is what I have loaded (they are all on the weechat scripts site, just google the filename and "weechat):
perl/autoload/:
bashorg.pl@ colorize_lines.pl@ notify_send.pl@ sysinfo.pl@
beep.pl highmon.pl@ perlexec.pl@ volumeter.pl
python/autoload/:
autosort.py@ colorize_nicks.py@ fullwidth.py@ otr.py@ ws_replace.py@ zncplayback.py@
bandwidth.py@ edit.py go.py@ urlgrab.py@ xfer_setip.py@
chanop.py@ emoji2alias.py@ ichatts.py@ vimode.py@ zncnotice.py@
ruby/autoload/:
mpdspam.rb@
[0]: https://weechat.org/scripts/source/highmon.pl.html/