Yes. ArcPad does the following to incoming GPS coordinates:
1. Transforms the GPS coordinates from the GPS datum (usually WGS84) to the Map's datum. This only occurs if the GPS datum does not match the Map's datum.
The GPS datum is set in the ArcPad Options dialog box: Protocol page.
ArcPad's datum transformations are stored in the file apDatums.dbf.
2. Projects the geographic GPS coordinates to the Map's projection. This only occurs if the Map uses projected coordinates.