Adding a new plugin which uses arrows shouldn't influence other arrow-based plugins; by your strand of logic, the currently existing plugins shouldn't work with each other. I'm fairly certain our sports plugins are independent from one another, so it shouldn't matter if a new one is added. (NOTE: I'm not a programmer and I don't know how the SRP plugins are written. This is speculation based on what I believe to be common sense.)
The way our resource pack works, this isn't an issue. Minecraft allows you to apply a custom model to the durability value of any tool/weapon, meaning you can have (basically) as many models as you want on anything, including the bow. We've actually done this on SRP, as you yourself have described; there are different models for baseball, basketball, and the "/am" command. There would be no issue in adding one more for an archery team.
These two arguments aside, I am personally against an official archery team on SRP. I agree with (mostly) everything that I haven't explicitly disagreed with that's been said by other people, but do have a few thoughts of my own to expand on the discussion.
Despite archery being a cultured and interesting skill, it wouldn't survive long-term as a subject of roleplay. It's a sport without much action, just pull back, aim, and release; no matter how it's written it will eventually become stale over time, and interest will die down. Inevitably, it would likely become an accessory to the characters participating, and not a serious sport worthy of notice; there's nothing wrong with something like this being ornamental, but only if that was the intention from the start.
Perhaps you could create an unofficial archery club, where it's more of a casual setting as opposed to a serious competitive sport. I couldn't say whether you could have a custom bow made, as ranged weapons aren't allowed; it may be difficult to obtain an archery range to use them as well, unless you have a property where building one would be realistic. Regardless, I think this is your greatest chance at introducing archery to SRP.