No they cannot. If you cut yourself open you could feel one if you could find something big enough to grab. Nerves in the scrotum are ultra small. It'd be like trying to feel individual hairs under your hat.
Even larger nerves like your ulnar nerve in your arm can't be felt from the outside. If you were to dissect your arm, it would feel like a fibrous noodle that goes flat when you squeeze it. They don't have noodle like density that the vas deferens has.