Yes, a half-day would be enough to get a feel and appreciation for Sorrento. However, if you want to include seeing the Amalfi Coast time may be an issue. The best way to see the Amalfi Coast is either by taking the SITA bus or to hire a driver to take you. For the purposes of saving time, I would think hiring a driver would be the most efficient manner to do this. If you do decide to do the Amalfi Coast plan ahead how far you want to go. The first stop will be Positano, and you could easily spend all day just there. The further you go towards Amalfi and Ravello the longer the trip back to Sorrento will be.
Capri would also make for a nice day, but again time will be an issue. Naples, this would be my last option for spending the day. If you head to Capri make sure you buy your return ferry ticket before leaving so you don’t miss your ship's departure. Capri is beautiful, but again you could easily spend all day there.
I would plan either the Amalfi Coast or Capri and do this as soon as you arrive. If you have time when you return then spend some time in Sorrento, this way you are not worrying about traffic or a late ferry and you’ll already be back in Sorrento.