I would like to start off that I would never think of running in a pair of Converse All-Stars or Converse Chuck Taylors.
But there is a large group of people out there that believe that the Converse Chuck Taylors would qualify as a minimalistic shoe.
I have a few issues with calling the Converse Chuck Taylors a minimalistic running shoe, they are too long and narrow, they don't really give you enough room to spread your toes. The shoe may be minimalistic in look but there sole is think and heavy. Also Nike has recently bought up Converse and added arch support and cushioning to the Converse chuck Taylor's.
There is a large group of people using the Converse Chuck Taylors to workout in, loving them for Dead lifts and squats because of their flat sole, but you don't see many running in them and I wouldn't recommend it.
A cool shoe? Yes
A running shoe? No