I'd have to say no to this idea. It would prompt more players to abuse the vote kick function because they could invite their friend to join rather than chancing another random. There needs to be that level of unsureness that makes the player think they need to be prepared to take whatever they get, they don't need to be given complete control of what party they go into or randoms getting kicked in favor of friends will become a huge problem.

On the other hand I wouldn't mind an option to turn off joining at the start if you specifically want to join in progress.