This is not striclty my area of expertise so I don't want to give you a bum steer - at best my response is vague but it may give you a few clues of where to start looking. I'm not too sure how you might have confgured this but your PDF form needs somewhere to send the data and then receive and store it - that's not a SharePoint list or document library (I seem to recall reading somewhere that you can do clever stuff with PDF and SharePoint but I don't think it works out of the box like you're describing here - that info basically alluded to using PDF and SharePoint together [like marketing statements] but didn't go into the hows). I suspect that submitting a PDF form may result in an XML data stream but don't quote me on that either. Alternatively if Acrobat is going to collate results then I think the form being submitted may need to end up in the same locaiton as the "master" PDF form but again I'm guessing a bit here too. For all intents the "master" pdf form may need to reside in SharePoint (and as a result it is addressable on a URL or as a file via WebDAV) in which case it will (or ought to) function like any other PDF form where you can collate results to a spreadsheet. If thats all it can do then using SharePoint seems moot. I think Google is your friend here :-)
Thanks for the reply, kpakrp. From what I've been reading on Google, it does seem that I'll perphaps need a few more pieces together to get PDFs and SharePoint to work happily together. I may need to get the server-side components of LiveCycle to really let everything work together. What our office is trying to do may be beyound the realm of a basic PDF form.