If I own a voice pack for a character my ally is playing but he doesn't, will the voice pack be applied so that I don't hear the default voice when he uses VGS? I don't own many voice packs so it would be hard for me to test.
Voice packs over VGS are dependant on the user, not other players.
So for example. if You own the voice pack for Ymir, but you are playing as Ao Kuang. You have an Ymir on your team, though. You will only hear Ymir's voice over VGS if the player using it owns the pack. It has nothing to do with you.
if you like how a voicepack sounds, but you don't play as the God. Don't get the pack.