RAW with Brotherhood of Psykers, if the Banner was used to activate a Terminator NFW, the Inquisitor would be left out in the cold, even if he joined the unit. He's still an IC, so he needs to activate his own weapon with his own warp charge.
The good new is that he still get the attack bonus. Also, if push comes to shove, the Inquisitor can "auto-activate" his force weapon with the banner if either the GK terminators burn their warp charge the old fashion way by rolling dice for their NFW or don't activate their NFW at all, e.g. Hammerhand.
More good new, the banner can activate any force weapon, not just NFW.
Now for the bad new.
If an Inquisitor takes the L1 Psyker upgrade, he
must take a vanilla force weapon. RAW No exception. That means either the Daemonhammer is going away or the psycannon/stormbolter goes away.
If the Inquisitor deep strikes w/ a unit of termies, he has to wait a turn to activate a Divination Power, RAW BRB page 67.
Still, not a bad bet. Since the GK Termies can load up on their own Daemonhammers, I'd leave the OM Inquisitor shooty.
Holy cow, this still looks very beefy on paper. A fully loaded OM Inquisitor is way less expensive than a GK Grand Master, Brother Captain, or even a Librarian, and adds a definitive punch to any Grey Knight unit. I'm going to have to try it out myself.