No, all the fields from LinkedIn are not automatically pulled into your database in anyway. JLinked will only pull the fields that you've 'mapped' in the Profiles configuration area.
Kunena and K2 both are 'fixed' as far as the fields they offer for you to import into. If you want a system that lets you create your own fields to import into, which will let you hopefully get the data you'd need, we'd recommend either JomSocial or Community Builder. Both are overkill for a simple profile system, but if you have to choose one, we'd recommend JomSocial.
Hope that helps explain, but if you need any more information, just let us know!
Thanks,
Alex