Quick question about this plot twist: If I am playing some characters with no team affiliation, can I use this card to make them part of another team?

I'm desperately trying to make an Arkham Exhaust deck using Thunder, Lightning, & Lockup but without sharing team affiliation, it just isn't working

Forced Allegiance
Plot Twist, 2
Choose a team affiliation from among characters you control.
Ongoing: Affiliated characters you control lose all team affiliations and gain the chosen team affiliation.

In order to be affected by FA, they must already have a team affiliation.