Not directly, but what you can do is create a CC Library for important projects or clients, and save fonts, brushes, colours, smart objects etc. to it. This is the way I go about it, and it is heaven not having to hunt through previous projects for a particular client to see what fonts I need to use.
Having said that, have user defined font groups is not a bad idea. If you go and suggest it on the Feedback site, come back and share the link, and I'll definitely add my name to it.
The alternative is to use a third party Font manager like Extensis Suitcase. I used to use and like FontDNA some years ago, but stopped using it because of the improvements they made to Photoshop. TypeKit was a great development, but I think you can only sync something like 10 fonts with a Photoshop only subscription. Its 100 fonts with a full subscription, but each weight and style of the same font counts as one of your synced fonts, so be careful.
Favourites is another nice development, but just being able to start typing con bo it for instance, will filter the list to Condensed Bold Italic fonts. I also love the new variable fonts. Purists will probably hate them, and they do feel like cheating, but by heck they are convenient to use.