According to the Warlord Trait, it states "select one of the Warlord's ranged weapons. That weapon gains +1 Strength and the Rending special rule for the duration of the battle." So it would definitely apply to a Conversion Beamer.
Aijec wrote:
I would argue that it would apply +1 strng to all modes but since there is no static statline and no precedent I can think of...
Rending would clearly apply
As stated above, it only applies to the Warlord's ranged weapon, and it would get Rending as well.