Yes and no.
You already linked it.
As documented, V5 supports querying by emoteset eg.
https://api.twitch.tv/kraken/chat/emoticon_images?emotesets=46
https://api.twitch.tv/kraken/chat/emoticon_images?emotesets=24414
https://api.twitch.tv/kraken/chat/emoticon_images?emotesets=24415
and also supports comma separated lists:
https://api.twitch.tv/kraken/chat/emoticon_images?emotesets=46,24414,24415
You can get emote/emoteset information like so:
which should list every available emote as well as its corresponding emoteset.
A single channel will usually have multiple active emotesets, as with the tiered example above, while an increasing number of sets don’t belong to a channel product at all. The current Kraken API doesn’t map the emoteset ID -> channel name relationship in the way you’re thinking. This is something you would either have to do yourself, as others have done before you, or with credit to Twitchemotes.com if using their API.