To start with AirPlay is based on the model ID string not the CPU your system has so this system just won't work. Apple does this often throwing a tease to get you to buy a newer system. Some of it is hardware related other times it's what they have tested the feature with. Here you have limits based on the hardware besides the CPU.
As to what you can upgrade the CPU with you are mostly limited on what Apple sold the system with. Remember Intel also has changed the sockets so you can't drop just anything in.
OK, here's what you have: iMac 27" 3.2 GHz - i3-550. So I'f we lookup on Intel's CPU chart: i3-550 chip we can see what it has.
Now let's compare it to the iMac 27" 2.93GHz - i7-870. Here we find Intel offered two versions i7-870.
So we need to dig a little deeper here looking at the TDP value the i3 is listed at 73 Watts. So you need the use a i7 that is this or less. The first version is 95 Watts so it's to high the S version is still too high at 82 Watts. So we can' go with the i7 version of the chip.
So now let's look at the i5 versions. Here's the specs for the faster i5 iMac: iMac 27" 3.6 GHz - i5-680
And here is the Intel chip info: i5-680. Now looking at the TDP we see the value is the same 73 Watts and we can see the socket is the same: FCLGA1156. So this is your only option.
Now you'll need to decide is it enough to of a bang to upgrade weighing the risks and the costs.