As you know, an inverted vee for a given freq is a balanced antenna with
essentially equal current and voltage on both legs. Grounding one leg
at or near the feedpoint will destroy that balance. Depending on the
height and freq, it will be omni-directional or directional broadside to
the legs. The angle of radiation is also dependent upon the height/freq
and angle between the legs (ideally a minimum of 110 degrees).
Using a balun ( I assume 1:1/ choke type) may or may not be beneficial,
depending on how close the legs are to the tower and the ground. It may
help keep RF from flowing on the outside of the coax. I'd just put it
up and see what happens.
GL, and 73
TowerTalk mailing list