I've had a Motorola Xoom (which doesn't support USB mass storage mode) for a while. Simply put, there is _no_ native support for MTP in OS X (10.7 or lower). If you plug your Galaxy Nexus into your Mac, nothing will happen at all. OS X won't see it, DoubleTwist doesn't see it, Songbird won't and iTunes (obviously) won't see it. As far as I know, there's no way of enabling your Mac to see the device natively, and all of the software designed for other MTP devices that I've tried doesn't work.
In fact, the only way your Mac will ever see it is if you download Google's Android File Helper software. This program, once installed, runs in the background, and whenever you plug in your Honeycomb (or ICS) device, it pops up a window showing the contents of the phone's memory. From here (and only from that window), you can pull files from the phone/tablet or put them onto it.
This works acceptably, but with a few hangups. First, unlike a normal finder window, only one transfer can occur at once, and there's no queueing. So, if you drop one folder on to copy, you're not able to move anything else onto or off of the card until it's finished. Also, large transfers (~10 GB) don't work particularly reliably, and may fail partway through, so you may consider dragging files in in groups. Finally, and most frustratingly, it will often not be up to date with what files are on the device, especially if you've recently deleted them. So, folders or files may still show up that you've recently deleted. Maybe this has been changed in ICS (I hope so!), but that's my experience.
That's your primary way on or off the device. I've had limited success using DDMS for transferring files on and off of the device, and although it's clunky and requires USB debugging mode, it's the most reliable way I've found for transfers that fail in the Transfer client. In practice, I'd recommend using something like SwiFTP to copy (smaller) files to and from your device, and avoiding the hassle when you can.
In short, you definitely CAN use OS X to transfer files onto and off of your Galaxy Nexus, but it's not as easy as it was for Gingerbread Devices, and tools like DoubleTwist and Songbird can no longer access your device at all (in their current versions). You can get around this using AirSync for DoubleTwist to load music, or doing so manually, but it's kludgey. It's unlikely that Apple will choose to support MTP in future versions of OS X (it's a Microsoft protocol now used mostly by Android), but hopefully Google will improve the tool as time goes on.
Sorry if this is all well known and obvious, but if you were on the fence about the GNex because of this, don't be. The MTP switch is annoying, but nothing showstopping, even for OS X. Just FYI.