  Accretion via disks can make neutron stars in low-mass X-ray binaries (LMXBs)
fast spinning, and some of these stars are detected as millisecond pulsars.
Here we report a practical way to find out if a neutron star in a transient
LMXB has reached the spin equilibrium by disk--magnetosphere interaction alone,
and if not, to estimate this spin equilibrium frequency. These can be done
using specific measurable source luminosities, such as the luminosity
corresponding to the transition between the accretion and propeller phases, and
the known stellar spin rate. Such a finding can be useful to test if the spin
distribution of millisecond pulsars, as well as an observed upper cutoff of
their spin rates, can be explained using disk--magnetosphere interaction alone,
or additional spin-down mechanisms, such as gravitational radiation, are
required. Applying our method, we find that the neutron star in the transient
LMXB Aql X--1 has not yet reached the spin equilibrium by disk--magnetosphere
interaction alone. We also perform numerical computations, with and without
gravitational radiation, to study the spin evolution of Aql X--1 through a
series of outbursts and to constrain its properties. While we find that the
gravitational wave emission from Aql X--1 cannot be established with certainty,
our numerical results show that the gravitational radiation from Aql X--1 is
possible, with a $1.6\times10^{37}$ g cm$^2$ upper limit of the neutron star
misaligned mass quadrupole moment.
