The jack on the Xbox 360 controller is a 2.5mm combination mic/mono speaker jack. I haven't tested this myself, but I've read that the pinout on the headset connector is mic/speaker/ground going from the tip towards the cable.
Microsoft doesn't really publicly specify the characteristics of mics that can be plugged into this port. No doubt there are some specs, so I can't say for sure that any generic mic plugged properly into this port would work.
When a headset is plugged into this jack, the game audio continues to be routed to the A/V connectors (ie, Component, HDMI, and/or optical) on the rear of the unit, but any voice chat audio is routed to the mono speaker jack on the controller. Without a headset, all of this audio is routed to the A/V connectors on the rear. Therefore, you can't plug a headset into the jack on the controller and turn the TV volume all the way down and expect to hear the game audio. Likewise, I don't believe you can plug in a mic and not a mono speaker to this jack without killing voice chat audio.
You can try to somehow mux the TV's (or your receiver's) audio into the voice chat audio in some fashion, but that can be a challenging DIY project. Just plugging it all together might work, but controlling relative volumes and signal issues/current flows might get awkward or complicated without at least a rudimentary knowledge of audio electronics hardware.
There are also third party headsets that handle this connection for you, and I've heard mixed reviews of such devices, so make sure you look into reviews of any specific models before you make a purchase.
What I personally use is an Astro Mixamp which is a wireless device that connects to the TV (optical), the controller, and a standard PC headset, and properly routes the audio around the room. You say you've already got a good Sennheiser headphone set - this is exactly the setup I use at home, a PC151 hooked to the Mixamp and my controller/the TV.
Sure enough, after switching out the Play and Charge Kit with a known newer one, the pairing delay was dramatically shorter, so much so that it paired while I was still at the profile selection screen, and sometimes it connected even before the avatars loaded.
Looks like I'll be buying new Play and Charge Kits in the not so distant future. I imagine that waiting 3 minutes to play games using all 4 controllers is going to get really old, really fast.
Best Answer
You can use standard headphones to listen to game sound, but not by connecting them to the controller. You would need to use a television with a headphone jack, and then jack into that.
Some fancier headphones will come with an optical hookup, which can be connected to back of the Xbox itself. I have a Turtle Beach gaming headset. It connects to the controller for the voice communications, and the Xbox for the game audio.