Can a timing belt replacement cause damage to camshaft?

I had my timing belt replaced at the dealership - when we got our car back, it had significantly less power - after many many many days of them trying this part and that part to fix, they finally told me I needed a new transmission? So, put new transmission in and is still slow/ stalling now - so NOW - they say it is the camshaft position sensor? I believe this is all related to the initial timing belt replacement and they did some damage - is that possible? Also, if the CPS is bad - would that warrant a new transmission?