The work factor is an input to the digest function, both when creating and when validating the password. Normally it should be stored alongside the digest itself so you can increase the work factor over time without disrupting existing passwords. So you are correct. It might theoretically be possible to correctly balance the work factor to counter variation in password info entropy so that all passwords take about the same time to crack, and this would be very cool and impress members of the opposite sex, but it would not improve security at all.
Making a probabilistic password checker is also a superficially interesting idea. Maybe my mind is too small to explore it completely, but it seems that at best it would be no better than just increasing the work factor.