Does a deactivated iPhone 4 still have GPS capability? I just got my iPhone 5, and I deactivated my iPhone 4. I am wondering if I can keep my iPhone 4 as a iPod that I run with.  Question is can, my Nike+ app still accurately track my runs?

I would much rather continue using my iPhone 4 running equipment (special case, armband, etc) instead of going to buy new stuff.
Yes, the GPS does not need cellular data or cellular service to work. It will get better results when GPS is offline if it can poll the location database and trilateralate from both Wi-Fi and cellular towers, but GPS is generally better than the these secondary sources of location data.

The phone should connect to Wi-Fi regularly to keep the location database up to date - perhaps while tethered to your iPhone 5 for optimal results.

For most situations it will work almost as if it were connected to cellular data and the cellular data switch was off.