Are donor and supporter mobile phone numbers automatically collected?

Yes. When somebody texts one of your keywords to the correct shortcode, their mobile number is automatically collected. This applies to all kinds of keywords on any of the shortcodes (41444, 51555, 71777, 91999)

Constituents that interact with keywords on these numbers will be automatically subscribed to a new list in your Manage Lists page accessed by going to Communication & Marketing > Manage Lists.

Communication & Marketing > Manage Lists