Isn't the biggest problem, here, that we're talking about two different things?
Text messages are SMS.
That's something that your carrier handles.
iMessage/Skype/any other server-side messaging system would be more aligned with MMS.
That's a data service that would require an app or OS-level integration.
Personally, I hate when people send text via MMS (group messages, for instance).
If you're sending a picture, use MMS.
If you're sending plain text, use SMS.
I don't think the operating system has access to SMS, until it is downloaded to the device.
That's why outlook.com could view text messages that you already had or sent.
But it wouldn't show new messages, if your phone died or was lost.
JJ