Unfortunately this is not something that can't be done.
Riot KateyKhaos pointed out the problems with something like this when she responded to a ultimate skin idea for Zyra.
http://boards.na.leagueoflegends.com/en/c/skin-champion-concepts/xkV06UJg-zyra-ultimate-skin-idea?comment=000100000000
[{quoted}](name=Riot KateyKhaos,realm=NA,application-id=A8FQeEA8,discussion-id=xkV06UJg,comment-id=000100000000,timestamp=2016-04-05T22:01:38.993+0000)
I'm not super techy, so bear with me!
It would depend on how the models for her plants would swap out. Champion models are fairly easy, but she also has models that interact with each other with her skills.
The other issue is, the content would need to stream and not be loaded into the game all at once, so that'd be something to keep in mind. Reason being, if we're loading in 4 Zyra's into a game at once, that's 3 extra champions, and it's something that lower spec computers may not be able to handle too easily. :P (Sona's music streamed, so it make it a bit easier for lower spec machines to handle!) Oh, and picture something like this in Hexakill for lower spec machines - probably not fun. D:
That said, swapping out let's say 9 models 'cause that's what Haunted Zyra has, and this would likely be as complex, if not more, it could cause a bit of lag if you're swapping whenever you'd like.
The game would have to load every champion that was selected and all their abilities then keep them on standby until they were used. This would be a problem for lower spec computers who might not have the RAM needed for this to happen.
The idea is very interesting and one I would love to try out, but there are limitations that prevent us from being able to play a mode such as this.