You do not want to change your GPS datum unless you know for certain what you are actually receiving as far as your corrections are concerned.
You can change your Status Bar Coordinate Format by going to the ArcPad>Options dialog and setting your Coordinate Format to: Projection.
You do not have an ArcPad project open, so there is no projection file to provide the correct information.
If you use ArcPad Data Manager and do a Checkout of data from a geodatabase, does the same happen? I am using Leica Zeno Field and using an project from the EasyOut process and I am able to utilize the projection coordinate format as you can see in the image below.
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