I'm not on Copaxone, but my expensive, on patent, ms med costs me $35 per month. That goes to my out of pocket maximum not my deductible for reasons I don't understand, so I pay it even after maxing out my deductible every year.
My experience with Kaiser is that they have covered all the bases in terms of care. They don't have ms specialist neurologists, which is frustrating at times. But, my general neuro seems extremely knowledgeable and creative with trying different meds for symptoms and also helpful with referrals to other departments when called for. I can give you his name, and or the name of a neuro with a very good reputation re MS within Kaiser if you want to message me. I chose not to switch, but considered it.
Re Kaiser primary care docs, they vary widely. When I was diagnosed, I switched providers as my original doc had ignored and minimized my neurological symptoms. I asked for a suggestion of a name from someone familiar with the system and am very happy with the care I get now.
Hope this helps.