  It has recently been suggested that collisions of transversely polarized
protons and antiprotons at the GSI could be used to determine the nucleon's
transversity densities from measurements of the double-spin asymmetry for the
Drell-Yan process. We analyze the role of higher-order perturbative QCD
corrections in this kinematic regime, in terms of the available fixed-order
contributions as well as of all-order soft-gluon resummations. We find that the
combined perturbative corrections to the individual unpolarized and
transversely polarized cross sections are large. We trace these large
enhancements to soft gluon emission near partonic threshold, and we suggest
that with a physically-motivated cut-off enhancements beyond lowest order are
moderated relative to resummed perturbation theory, but still significant. The
unpolarized dilepton cross section for the GSI kinematics may therefore provide
information on the relation of perturbative and nonperturbative dynamics in
hadronic scattering. The spin asymmetry turns out to be rather robust,
relatively insensitive to higher orders, resummation, and the cut-offs.
