Thanks for the question!
If this was a simple answer, I could give it easily. It's not a simple answer, I'm afraid. There are a LOT of levels to it and the deeper I get I fear that folks will get hung up on the specifics and miss the overall picture.
Specifically, you're asking about "playing AGAINST", not "playing WITH" or "playing AS". I don't think a conversation can be had about any one of those things without the others and - honestly - I don't feel comfortable answering that question because it's just not how WG calculates stuff or how decisions are made.
So, the short answer is YES - we do factor in feedback on how it feels to play AGAINST something, but that's mostly something that results in action for a balancing aspect and adjusted when necessary. This feedback comes from a variety of sources when new ships come out including Community, SuperTesters, Clan SuperTesters, Privateers, Community Contributors, and staff.
Often times new things "feel bad" to play against because we, as players, don't understand their boundaries yet. I recall absolutely hating to play against Conqueror's for a long time. They'd spam HE and superheal and I thought that was crazy. Then I played against them in clan battles and realized that they go down extremely quick if they get focus-fired. Their weakness is being burst-fired and not having the time to utilize more than 1 super-heal. It's much easier to do that with a team that you organize and can agree to a plan, which is much more difficult in randoms.
I hope that helps a bit, but I just cannot give out a simple answer to that question as it is, I'm afraid.