What is GW's expected behavior when a mailbox reaches the warning
threshold? Is GW 2014 designed to send an email message to the user -
or is the warning only offered to the user when in online mode or
webaccess, and attempting to create a new message?

I'm asking because users are sometimes exclusively using mobile devices
(via GMS) - and one of my users recently sent out a fairly large number
of messages that way, which were never really sent because she had
exceeded her mailbox size limit. Messy.

So - if GW is working properly, will it send an email message to the
user whose mailbox has reached the designated warning threshold? If the
answer is "no" then I will put in a feature request. (And you should,
too, if you have size limits and mobile users.)