Do support gems override or extend the "type" of attack skills

It sounds intuitive that when linking a support gem to a skill gem, the support gem can in a way alter the type of the skill. For example, it makes sense that linking a Ballista Totem Support to a Galvanic Arrow will make the skill benefit from effects that increase totem damage.

What's less intuitive is whether the skill altered this way still benefits from effects that boost the original type of that skill. To use the previous example with Ballista Totem Support and Galvanic Arrow, will taking passive skills that increase bow damage affect the damage of the totem as well?

The wiki page of the Ballista Totem Support says:

Totems use the player's own skills as though the player had cast them, ...

... which would imply the skill will still benefit from increased bow damage, but it doesn't directly confirm or deny it. I'm still new to the game and would really prefer a confirmation before spending my hard-earned skill points (considering how hard it is to unlearn passive skills).