My concerns have to do with the fact that you are totally reliant on other companies (ISP, Microsoft / Google) for the ability to do your job. If this takes off it will only be a matter of time before ISPs start going after Office 365 or Google Apps traffic like they are going after torrent / Netflix traffic now. They will say that it is taking up to much bandwidth and they will impose harsh data caps or charge absurd amounts for not throttling your speeds.

Also your information is out of your control. Your information security is reliant on Google or Microsoft's information security and we all know that new flaws are found in Microsoft products and Gmail is hacked all the time.

Finally your if your ISP, Microsoft, or Google have downtime you have downtime, and their isn't a thing you can do about it but wait until the problem is fixed. .

Is it possible to run your company via online subscription service? Yes, but to factors make it impractical and almost downright dangerous.