Most airlines I have used, have a size, weight and number restriction on cabin baggage. It varies from airline to airline. Most also have a metal gauge next to the boarding gate, with the rule that your bag must fit into the baggage gauge including handles, pockets and wheels. To me, your Boundary bag + "Aux compartment" certainly looks like one bag with a pocket, and if it fitted in the gauge I doubt there would be a problem.
That said, you might have a problem if flying with an airline that rigidly enforces a one bag policy. With the growth of low-cost air travel, charging passengers for bags put in the hold is a useful revenue stream. I seems to me that some go out of their way to try to force you to put your otherwise quite OK cabin bag that you have used for years, into the hold (and then charge you €50) because they have started counting small purses or the plastic carrier you bought your duty free in as your one cabin bag. Some airlines are worse for this than others (yes, I'm thinking of Ryanair!)
The only real way of finding out for sure is to ask your airline before you fly, and maybe before you even book your ticket.