6S works well with the CC BEC Pro. The BEC Pro is rated for up to 12S, but there have been isolated reports of the BEC Pro failing when exposed to such high voltages. You also get more output current on 6S than on 12S (see pic below).
Interestingly, when powering the BEC Pro on 6S on a 12S setup, the mah consumption on the pack powering the BEC is not a whole lot. My Whiplash consumes an average of 52mah per flight powering the MKS HBL 950/980 HV servos at 7.5v. The E7SE consumes an average of 57mah per flight powering the Futaba BLS255HV cyclic servos and MKS HBL 980 HV tail servo at 7.5v, and E5s consumed an average of 73mah per flight powering the Futaba BLS255/256HV servos at 7.5v. So according to those numbers, the MKS HBL 950/980 HV servos are not as power hungry as the Futaba BLS255/256HV servos. Still, non of those servos have caused any brown-outs when powered by the BEC Pro on 6S at 7.5v. However, not all servos are made equal. When performing the VBar power test at the bench, I can cause a brown-out when powering the Align DS610/650 servos with the BEC Pro on 6S at 6v on my T-Rex 550. The Align DS610/650 are coreless and known to not be very efficient, so this is not surprising. Still, no problems in flight with those Align servos.
It is also best to run the BEC Pro on 6S rather than 12S because you get more output current on 6S.