Not recommended — #30 of 31 Wool ranks #30 of 31 fabrics for quick drying. It is a poor fabric for this. Ranked on low moisture regain, low weight, and packability — the inverse of absorbency. The top pick is Polypropylene.
Wool measures 55/100 for breathability, 15% moisture regain, 85/100 warmth, at 280 gsm. Fast drying favours low moisture regain: at 15% Wool holds water and dries slowly, and 280 gsm keeps it light.