Eh, I don't think that's really what OP is suggesting. they want to abolish character sheets, but they seem to understand that GMs need some metric to measure the characters by. 

A free jump-in RP could work, and has in the past. But it requires some very specific parameters. You need to be okay with one liners and people who can barely write English, Then you need a plot where a character's powers and background can't be used to gain an advantage, or people have no ability to use magic/anything, or whatever powers they have are exactly the same for everyone. The only thing that comes to mind is maybe a "slice of life" RP where it's just about all the characters trying to live together under one roof and tolerate each other. You could maybe do generic adventure stuff, but it would either be a power fantasy or a chatroom type of RP, neither of which are really my cup of tea. 

I suppose if you wanted an alternative to a character sheet, you could always jump into a chat with the GM and talk about your character. But I would ask for the same information my character sheets require, and I think most people would find it overly personal/confrontational.