Not really, although it depends what you consider to be a "role". The important thing to understand is that the Taliban were not a direct successor to the Mujaheddin that had fought the Soviets in the 1980s and enjoyed semi-clandestine American support. Although their membership absolutely included former members of the Muj - which in turn would have included men who had enjoyed American-supported training and arming - the majority of the organizational components of the Muj took control of the country in 1992 in a power-sharing arrangement as the government of Islamic State of Afghanistan. Civil War continued however as not all of the groups could get along, and the Taliban was formed in this period as a "third way" group that positioned itself against both existing sides of the Civil War. They would eventually kick out the Mujaheddin-originated government in Kabul whose leaders took to the hills and continued to fight as the Northern Alliance.

So while it is eminently fair to say that people who had enjoyed American support ended up in the Taliban, and also that the effective end of American aid to the Mujahideen once the Soviets left helped to create the post-Soviet period quagmire that allowed the Taliban to flourish, there is not a direct genesis from the American supported groups to the Taliban, and that mantle rightfully belongs to the Northern Alliance which fought against them. For some expansion on this, I wrote a piece awhile back which you can find here and fleshes things out a bit more.