This is an interesting question and one that I am seeing different options on the various phone platforms we are testing in our company. We have an Exchange 2010 environment and testing with 3 mobile OS's (Windows Phone 8, Android 4.2.x S.A.F.E. phones & iOS 6.1.x) and seeing 3 different results.
iOS devices (native email client) - able to see all drafts created in Outlook (syncing 3 months of email), but cannot send them (only Forward, Reply & Print).
Android 4.2.x devices (native mail client) - able to only see drafts created today, but can send, edit, forward and add addresses for To:, CC: ...
Windows Phone 8 devices (native email client) - able to see all drafts, send, edit and full functionality
Even changing the Outlook options to save draft emails to the Draft folder, Inbox and Sent - similar results. No settings in ActiveSync to limit drafts and no settings in our MDM Solution (AirWatch release 6.2.1.7) preventing this activity as well for any OS.
I would think that it is a mobile OS constraint and not EAS, since we are seeing varying results from the devices connecting all the same way.