When Google launched Inbox last year, it was offered exclusively to users who received an invite to their personal Gmail account. Google Apps for Business (or Education) users weren't allowed in on the fun, which seemed rather weird but understandable. After all, the new email organization and interaction paradigm was built with productivity in mind, and business users are the ones that would benefit the most from that. However, since this was an entirely new app and system, it was judicious of Google to test it out with a less demanding crowd first.
— sundarpichai (@sundarpichai) February 19, 2015
Sundar Pichai shared on Twitter that this discrimination against Google Apps users is going to be stopped, "imminently." After expanding to both the iPad and several browsers beyond Chrome, Inbox will soon be available to Apps accounts (presumably, also pending the reception of an invite).
I just tried sending myself an invite to my AndroidPolice email address, but upon switching to the account in the Inbox app, I get told that Inbox hasn't been activated for me yet and sent to this support page that still states that the service isn't available for Google Apps users. I guess it isn't live yet, but it should be soon.