Can I use the white neutral wire in a 14/3 cable to carry hot power for a 3-way switch?

You can only use that white wire to carry hot power if it's re-identified with black electrical tape as a hot traveler—never leave it plain white, or someone working on that box later will take 120 volts to the hand. Upstream, modern electrical code requires a dedicated neutral in switch boxes for smart switches, so robbing that wire often leaves the circuit out of code. If you aren't sure how to trace your lines with a digital multimeter, hire a licensed electrician to rewire it safely; electrical modifications usually require a permit and guessing wrong can easily start a fire.