So I have to stand corrected here. I dug through some old posts to correct my memory. Your boarding position (including if you purchase a single EBCI for the non-A-list CP holder) on non-BS fares will carry through to a companion's boarding position to ensure that you are boarded sequentially. Having CP alone without either party being an A-lister will not get you a good boarding position (minus checking in at T-24 which is good enough for me, or purchasing EBCI).

That being said, I still think that having a CP is exponentially more beneficial than A-list. Spend a few extra bucks on EBCI if it is a big deal or one is traveling alone. Using a CP even once a year should more than cover that cost.