Is it possible to play only custom maps?

Yes it is! - however, currently there is no system in game (either through the phone or the menus) that will allow you to just join games running on custom maps.

To play on custom maps, you currently have to go through the Rockstar Social Club website, which should already be linked to your console account if you're playing online, then select "games", "Grand Theft Auto V", "GTA online" and then "jobs". At the top there are some drop down menus - filler these to social club members and you will only see community made maps.

It is not currently possible to play multiple custom maps in a row so each time you want to play a custom map (even if you've just finished one) you will have to go through the Rockstar Social Club. With any luck this additional functionality will be added in a future patch although there has been no announcement from Rockstar to this effect at this time.