Gun Damage affecting Grenade Damage weapons?

There are some weapons that are improved by Grenade Damage bonuses, like the SWORDSPLOSION and KerBlaster.
Do these guns gain any benefit from Gun Damage bonuses?

Grenade damage multiplies gun damage. Given a choice between the two, gun damage will net you more damage than just grenade damage.

The grenade damage bonuses are on splash…and they are decent but not overwhelming.

ALWAYS go for higher gun damage and you can’t go wrong.