see section B of https://eprints.soton.ac.uk/267873/1/tcas1_cordic_review.pdf. Generalized cordic can compute hyperbolic trig functions which gives you exponentials. That said, it's still not useful for ML because it's pretty hard to beat polynomials and tables.
I don't immediately see how cordic would help you calculate e^(x) unless x is complex valued (which it is usually not).