Both Smiths and Road Town Fast Ferry definitely pick up at Spanish Town in the mornings (reservations are required) but I believe only Smiths pick up on the afternoon run.

RTFF run on Mon/Wed/Fri and Smiths run on Tue/Thu/Sun.
http://www.bestofbvi.com/info/bviferry_vg_anegada.htm

As with all ferries, I suggest calling them beforehand to verify they will be running to schedule.