I have a 2wd and have traveled on a lot of unpaved, rough roads. But these were graded routes. But I know I am limited and have turned away from a number of unknown routes/paths.
Sure it can do well on a 2-track path but you need to know it's condition ahead as well as the current condition (wetness). It would be wise to carry a tow or recovery strap.
A 2wd simply does not compare to a 4wd when traction or footing becomes marginal.