Yes, something like that would do. However, it might be better to load the
template by adding it to the AddIns collection. All add-ins are also members
of the Templates collection, and you can identify them as such. Something
like this

Addins.Add FileName:="DriveSpec:\path\MyTemplate.dot", Install=True
Set myTemplate = Templates("DriveSpec:\path\MyTemplate.dot")
MyTemplate.AutoTextEntries.Add Name:= strAutoText, Value:= strAutoText

Then at the end, you can do this

MyTemplate.Save
Set myTemplate = Nothing
Addins("DriveSpec:\path\MyTemplate.dot").Installed = False
Addins("DriveSpec:\path\MyTemplate.dot").Delete

This saves the changes in the template, unloads it and removes it from the
list of addins.

Nope, AttachedTemplate is the attached template, not a template that is
loaded as an Add-In.
You can only have one attached template. You can have many Add-Ins. For more
on the different kinds of templates, tabs on the file new dialog, and
locations of templates folders see
http://addbalance.com/usersguide/templates.htm.

If you want to be able to add AutoText to an Add-In the simple way is to
create the AutoText and save it to your template making sure that it is
going to your template. You can't do this with Shift-F3, you need to use the
AutoText dialog and specify the location. (Note, the location you specify
here sticks for the remainder of your Word session and limits not only where
AutoText goes but where Word looks for AutoText.) This is simple for you to
do. It isn't simple to train a user to do it. Especially not bulk users.
Also, if you actually share a single AutoText Add-In, the first person to
start Word will put a lock on the Add-In file. No one else will be able to
edit it. The preferred method to distribute Add-Ins is to put the file on
the network and have it copied to a local file upon login for use as a local
file.

Do you want you or one designated person per office to add AutoText but to
have everyone able to use it? If so that will work. If you want everyone to
be able to edit AutoText in your Add-In that adds a whole layer of
complexity and security. (If someone can edit, they can delete.) I'm not
sure it is possible. I've just had people email me documents containing the
AutoText they want added with a suggested name.