I'd like the tooltip to provide extra information as to why the button appears disabled. Is it a good idea to do this? The tooltip may get slightly hidden by the tapping finger...
Yes. This is a great idea!
Disabled buttons can be very frustrating to users if there is no clear indicator of why they are disabled. This can result in all kinds of negative behavior including frustration, abandonment, or bad anchoring where the user assumes the button is not a control or doesn't work (a particular risk with flat design where buttons are not always easily distinguished, as in your layout above).
It may be awkward to figure out where to place and style the tooltip, but this is a great example of thoughtful and empathic UX design. One thing you may consider is an auto-fadeout of the tooltop after a few seconds, so the user doesn't have to actively dismiss it.