Yes, but it's not totally ideal.
The Sirius S50 can record up to 4 hours of broadcasts to internal memory, which you can then listen to any time without a sat. signal.
You can set up timers like a VCR to record various shows.
The S50 itself cannot receive a satellite signal - it requires a docking station to play a "live" signal or record a show.
The silly thing with the S50 is that it comes with a car docking station. That's great if you want to listen while driving, but the purpose of the S50 was to allow you to record and listen later. If your car is turned off, unless you want to drain the battery, you are not going to be recording in your car.
So you need to fork out another $100 to get the home docking station.
Still, if they would lower the price a little I'd think about getting it. I would record music and shows at night, then take the S50 with me to work and listen to them during the day. Some of the live shows during the day replay at night, so you'd be a day behind, but that's life with satellite...