Were the Ephesians a portion of the divorced northern kingdom of Israel?

No. In Ephesians 2:11-12 Paul writes the following to the Ephesians:

Therefore remember that at one time you Gentiles in the flesh, called “the uncircumcision” by what is called the circumcision, which is made in the flesh by hands — {12} remember that you were at that time separated from Christ, alienated from the commonwealth of Israel and strangers to the covenants of promise, having no hope and without God in the world.

Paul makes it clear that part of the reason the Ephesians were previously ‘alienated’ (Greek: Apallotrioo [Strong’s 526]) from the commonwealth of Israel was because they were Gentiles (i.e. non-Jews, not because they had once been part of Israel but had somehow become “divorced”). Cf. Eph. 4:17-18, where similar language is used.