Sure, it's possible, but it would be a lot of work. The ArcPad object model gives you access to all the information you would need to do it, but I don't really see any helpful functions that would automate the geoprocessing (setting measures, etc) part of it. (Although the Point object does have a "measure" property, so maybe I'm just not seeing it.)
I'd start by checking out the "Line Object" help item in the Customizing ArcPad help, you can follow it down to "Parts" then "Item" within "Parts" then "Point" objects whose measures you can set and whose geographic location you have access to.
You'd basically have to break it down into its component parts and then rebuild it to the specified length, interpolating between existing vertices along the line, and then drop a point there.
Possible, but I wouldn't envy your task. 🙂
Hope this helps,
Eric