Unfortunately no this is not possible. The main issue here is that wordpress core doesn't support connecting users into relationships with Posts in the traditional sense.
This is due to the users already being in a relationship with the posts by being the author of that posts.
There isn't any coded workaround either as mentioned wordpress core itself doesn't support this. If a solution would be made it would involved Database modifications and the use of custom tables to hold the relational information.
You can get around this by allowing the user to create a profile post then relating that profile post to another post type.