The answer is clearly yes. This is e.g. treated in Hewson's book ["The Kondo Problem to Heavy Fermions", Cambridge Univ. Press (1993)) in Chapter 9.4 (pages 283-285 in my edition).

Very qualitatively, if we have a singlet ground state, then this naively would have no energy dependence on magnetic field (i.e. no moment) [it's not so simple because it is a many body singlet, coupled to a gapless excitation continuum (the metal)]. Simplified again, think of excited states as of triplet states, which must have Zeeman splitting. the Kondo GS then cannot survive arbitrarily large fields. Rather you'd expect that it is "destroyed" on the scale where Zeeman energy and kBTK become comparable. For any thought beyond this, consult the serious literature. Hewson is a good place to begin with.