So, I think there's a bit of confusion here. What do you mean by "manage" and "recognize"?
MC will certainly support such files. It will play them. You can add them, and tag them manually however you'd like, so they'll show up in the right views as the right shows and so on. If you want them to sort in the right order, you'll just have to put the range of episodes they contain in the [Episode] tag, like:
[Episode] = X-Z
(Using your example from above.)
I do this often with shows like the finale of HIMYM that are two "separate" episodes, which really have basically the same metadata anyway. So, for that example, I'd just tag it as:
[Media Sub Type] = TV Show
[Series] = How I Met Your Mother
[Season] = 9
(if your file is named somewhat nicely, the above is probably already done).
[Episode] = 23
Then, I'd do the metadata lookup, to pull details about episode 23 from TMDB. Then, I'd change that episode tag to "23-24" just to be more technically correct.
However, it won't automatically recognize the kinds of file names you mentioned, because MC is built where generally each database entry (typically each file) is individual, and assumed to be a single "unit" of media.
Carnac doesn't know about those kinds of filenames, as it does with many others, so it will not automatically parse them properly. And, since it can only look up metadata for a single database entry (single file, again, typically) then you won't be able to get accurate descriptions and whatnot for the individual episodes (or choose them individually within Media Center's views).
Particles, mentioned above, are designed to solve this. This is a bit of an advanced feature, but you can use Particles to "virtually" break-up single files into separate pieces. This would be much like astromo's suggestion of actually cutting them apart with MKVToolnix, but wouldn't alter the files themselves in any way. It is all done from within MC.
The idea of particles is that you tell MC that a particular file should be split up into these individual components (particles) which are then treated by MC as though they are separate files. For each particle added, you essentially tell MC to "only play this particular time range" within the file (27:42 - 55:15, for example). From there, you just need to tag them with [Series], [Season], and [Episode] and then MC will be able to look up metadata for each of them.
Particles can be created automatically if your files have chapter marks, but since you mentioned a bunch are AVIs, they probably don't (this is more typical with DVD and Blu-Ray rips). Assuming you don't have chapter marks, you would need to enter them manually, because otherwise it won't know where to start/stop each individual episode.
Once they're divided up into separate Particles, they'll work basically just like they're "real files" in Media Center, and you can run the Lookup TV Info tool on them to get the metadata. And, they'll automatically jump to the right spot when you play them back (and end at the end of the episode).