Our SP inquired on an issue similar, and was told by the respective GA that this is a matter for local authorities to determine. And, actually, hasn't that been the thrust, especially as of late? Direction SHOULD come from the local priesthood. Our stake uses Google Docs extensively. Every document used to create our big Stake YM events are stored in Google Docs so that when leaders change there is continuity, e.g., basketball tournament plans/schedules, Varsity tournaments for outdoors, plans for all past youth conferences. Our ward uses it as well.
We've also started using Agreedo to create agendas for meetings (wonderful tool).
With the Internet now in our clerk's office, the agendas and docs can all be updated anywhere by the leaders and then printed out locally at the clerk's office based on changes from meetings at the church that day. As soon as the 7 am bishopric meeting ends, we make changes to the online agenda for PEC or WC and then print it out in final form for the 8:30 am meeting. It's invaluable for us.
If a unit were to determine that Google Docs (or its equivalent) should NOT be use, then I'd also advise they stop using email to send any documents, because in essence that's all that Gmail (or other emails) is, i.e., a document archival service unless the user empties all sent/received emails and deleted emails consistently, and even then the data is still online for at least some portion of time. Every document that I've ever sent via Gmail is stored in my archive. EVERYTHING (which is wonderful since I can find information on all sorts of past activities, events, and notes for people no matter how much time has passed). If there's a danger that someone might hack into my account to get a doc saved by me in Google Docs, then there's also the same chance he gets to my online email archive and get the same document. In fact, the email archive is even MORE important since often there are personal items that are put into an email on a member's situation but would NOT be written on a document stored online and meant to be printed out.
If a person wants to make sure that certain information is never open to viewing by an unauthorized person (hacker), then stick to SMS (texts) or in-person communication (though even SMS is open to attack). All in all, I think some people worry about it mostly because they don't understand the 1s and 0s, and what data is. But if you did keep ALL your stuff offline, including the exclusion of email, it definitely reduces your risk of disclosure to near zero. Also, exclusion of electronic data means people won't be haphazardly printing out confidential items because distribution is limited to handouts (just don't leave that agenda on your books somewhere). My own view is that Google Docs and email increase the risk of improper disclosure but not to a level that is unreasonable. It's like going from 0 risk if you write nothing down to 1% if you use a typewriter, 1.1% if you email it and 1.2% if you use Google Docs. In other words, there are more important things to worry about than making things more efficient for everyone involved.
All very scientific methods, mind you.