With a film camera, classic or otherwise, I'd say generally no, it doesn't really matter. As long as the camera functions correctly, a film camera (any camera, really) is simply a light-tight box built to house a light-sensitive material and to allow light to enter in a controlled fashion. Or so I was always taught. Everything beyond that is bells and whistles.
With digital, I could argue — tentatively — that which camera you shoot can matter. With digital, it's as much about the software/firmware of the camera, how it handles the information, size of sensor, quality of sensor, etc, ad infinitum, as anything.
But, that does not take into account the photographer. That's all technical crap. So, I could also argue it doesn't matter what camera you use, as long as you are familiar with it, comfortable with it and enjoy shooting with it.
I don't know how many times people have told me they love my camera and that it must take really great photos. I tell them, no, it doesn't do a bloody thing by itself. I'm the one that make the images. The camera simply records them, be it digital, analog, new, old, or whatever.
It's the artist, not the tools. So, find a camera you are comfortable with, can work with seamlessly, and enjoy working with. From there, the sky's the limit!