It depends on how narrow your definition of a soap opera is, I think.
Is it a soap? No. But as you so rightly point out, NuWho certainly mines elements of soaps - they spend a lot more time on characters relationships and emotional journeys far more than classic Who ever did.
Which I don't regard as a bad thing, by the way. Indeed, I've made this point in another thread - I felt the first and third episode of the new season would probably have worked better without the overt intrusion of scifi elements.