Yes, you still try to wake the person up, check for breathing and a pulse, and check the airway for obstructions. Although we are now taught to NEVER do a blind finger-sweep for an obstruction. We should only remove something if it is in plain sight and easily grasped. With a blind finger sweep, you're as likely to lodge the obstruction more firmly in the airway as to remove it.

I also carry a barrier with me, but only plan on using it if a second person is with me. If I am alone, I'll only be doing compressions. Good compressions seem to make a bigger difference than rescue breaths, and stopping compressions every 20 seconds, doing a head tilt, repositioning the barrier, and providing two breaths seems detrimental to good compressions.