At our organization we're just now looking into caching data for ArcPad.
Research on support forums & the ArcPad team blog suggests that ArcPad can use cached data from AGS so long as it's in 3857 projection and uses AGO tiling scheme & exploded format.
Can ArcPad use tile cache or tile package? I assume not since this idea is not yet marked for consideration or implementation. Are there any upcoming plans to support them? These formats would make it much easier to get cached base maps into ArcPad, without involving AGS at all.