We can in my airplane:
Quite frankly, I'm usually a little insulted when it happens.
Were they actually so fearful for their lives and are now so happy to be alive that they need to applaud the heroic pilots? Sorry, but unless it's a true emergency and we did actually just save their lives, I'm not putting them in a situation where they are actually at risk. In this case, I was just doing my job. Do you applaud the waiter or waitress who gets your order right?? :-)
As far as airliners, I'm pretty sure that the pilots can hear you too if everyone is clapping but someone with experience on that should confirm whether or not this is true.
Disclaimer: This isn't the actual airplane that I fly, but it is the same kind. Notice also that we don't have a door to our cockpit so this makes it much easier to hear what is going on in back.