Not exactly. No necessity to use BEC, most of us do to avoid having to fit another pack of batteries, but far from essential. Sometimes a BEC can be inadequate for the current drawn, and that can cause issues, so that's why I was asking.
As you are powering them direct from a 6volt battery, current draw shouldn't be an issue. it's possible, although unlikely that you may be overpowering the servos, as a freshly charged 6 volt battery can push well over 6 volts, and beyond that figure, many servos can start to complain.