I'm in a sleepy state, so i'm not concetrating too hard, but off the top of my head here's a few champs who I think would be troubled by a PvE game mode:

Fiddlesticks
Akali
Nunu (I guess you could just support with Bloodboil and throw your iltimate, but eh)
Blitz (Until you get his ult, but that's his only wave clearinf ability. Also, fist becomes useless)
Evelyn
Irelia
Leblanc
Nidalee (Albeit I think her cat form has a AoE effect or something, so less so here)
Poppy
Shen
Sona
Trundle

A few of them i'm unsure of, but put them there due to a lack of AoE or heavy pushing power. Some champs, like WW, who lack AoE/Wave cleared effects but can merely sustain and smash open a lane anyway from sheer punchingness. Aside from that I don't have much else to contribute. It'd be nice to have a game mode like that, but it'd definetely be treated as secondary in comparison to even the other game modes. Something more for laughs and derping around then actually playing League.