Yes, provided the nature and timescales of the dynamics are the same it should be safe to use the same thermostat (and time-step, barostat etc) parameters for the ab initio MD and the classical MD. The thermostat parameters are chosen according to the characteristic times for the dynamics, they don't particularly care what the details of the dynamics are. If applicable, you should make sure you're using the same constraints and restraints in both simulations, as they can also affect the timescales of the dynamics.
There are some exceptions, such as if your classical MD used a coarse-grained model; in that case, the classical dynamics would be much slower than the ab initio dynamics. I'm not quite sure whether you'd have to do anything different if you were actually doing Car-Parrinello dynamics for your AIMD, since in that case the ab initio dynamics would include electron (really, Kohn-Sham particle) dynamics, which are not present in classical MD and happen on a much shorter timescale. Those dynamics might be integrated out well enough that they don't affect your thermostat etc, but it would be worth checking.
One difference between AIMD and most classical MD is the possibility to change the atomic interactions dynamically, e.g. by breaking or forming chemical bonds. If this happens during your simulation, then you may want to check the time-step and thermostat parameters again, because this could affect the time-scales signficantly.