Not necessarily. It comes down to an impedance ratio. I call it the 10:1 rule. In commercial installations it's not uncommon for a single output to drive multiple amp input channels. What you're doing is exactly the same as a parallel input/output on an amp or a powered speaker.
I have to make some assumptions here since I don't know exactly what you're using (although since I sold you much of it I think I'm going to take some liberties with these numbers). Let's assume your mixer's output impedance is 100 Ohms and the powered speaker's input impedance is 10,000 Ohms. That's a ratio of 100:1, so in theory we could connect 10 of those speakers to that drive in parallel. I might be oversimplifying it a bit here, and I'm sure some of my fellow nerds will jump in to try to complicate it, but that's the basics of it.
Where it gets a bit messier is when you talk about driving both a powered speaker and a recording device, which may have different input impedances and also different grounding structures. A transformer based splitting device would be a preferred way to avoid any problems here. Many times in FOH snakes when we split an input signal between a FOH console and a monitor desk we will use Ground Lifts (GLs) and Isolation Transformers (ISOs) to ensure that we don't invite problems into our mix (pun intended).
That help?
Ben