In short, yes, if it is a current-fed antenna, i.e. a quarter wave, or odd multiple thereof (3/4,5/4, etc.); if it is a λ/2 antenna, or even multiple thereof, then no, it does not need radials.
Whether or not your λ/4 HF vertical antenna uses a loading coil, it will benefit fromfrom radials, but at a minimum, must have a counterpoise.
You may also be interested to check out the question, "What do radials really do for a vertical antenna?" and its answers for additional relevant information!
