Can you still get Nemesis Icon if you had to restart client?

A question I have regarding the Nemesis icon: Can I still get the icon even when I have to force the client to shut down to reboot to fix a client issue?

Specifically, for well over a year (probably more like 2 years), I occasionally get an issue where my hot keys do not work. I have bugged this more than once and I know others have bugged this as well. As far as I know, Riot has never once responded to or acknowledged the issue. I assume this means Riot doesn't particularly care about creating the worst playing experience for their game possible (literally, qwer, fd, 1-7, b...all your hot keys needed to play do not work in normal game play but do work in chat), but that is a separate discussion.

The only way I know to 'fix' the issue is that I have to completely shut down LoL and restart the game. It happened again to me just now while in Nemesis mode. I do the restart as quick as I can, but it still means I have to shut down LoL. In this case, I actually had to do it twice (rebooted the entire computer the second time) before my hot keys would work. Does that mean I just lost the ability to get the icon?

And in the greater scheme of things, how does the issue of needing to restart a client like this work for the new leaverbuster or whatever it's called?