You may have trouble with an Otterbox. I have a Samsung Epic with a Platinum case that isn't even as beefy as the Otterbox, and I found that my phone just barely seated on the USB connector well enough to get a power connection. It would do it, but one slight bump would be enough to jar it free. There are two plastic support posts on each side of the USB connector that are intended to stabilize the phone, but I thought that if I filed or ground them down with a Dremel tool, lowering their height might allow my phone to be better seated on the connector. That did the trick, although it so happens that while I filed both down evenly, the cutouts on my case allow the phone to tilt more toward one side. Not a big deal, just not as aesthetically correct, but the phone now gets a good connection so it will now charge correctly. Of course, my efforts committed me to keeping the AS111, but I decided for the $69 I paid at Best Buy, it would be convenient to have. If I ever swap phones, I think the two support posts might could be fully ground down if need be (although I found they are metal underneath the plastic) and replaced with two rubber or foam bumpers.
Not real sure about the otterbox but I have a case on my s3 and it does work. The micro usb has a knob on the side that allows you to extend it or retract it as much as you want. My best guess would be yes. Good luck!