Not it does not. You're judging power handling of your AVR based on its power draw at the socket! How does that even give you a hint that all is well with the power being delivered to your loudspeaker?
Pick any modern day receiver with a power save mode. They refuse to budge outside their power threshold no matter hard you drive them. Are your speakers going to like this? Absolutely not.
Typically, most cross over our sub woofers at 60 or 80Hz for home theater applications. That value is a personal preference. When you do this, a majority of bass is handled by the sub woofer, not your main speakers or any of the other speakers. Your amplifier is relieved of this load. Most sub woofers sold today are more efficient than Class AB sub woofers sold over a decade ago. Their power draw isn't going to be much at all anyway. A peak will register as a tiny blip for a second at the most.
Its a different matter that you were unable to register a difference by adding a power amplifier. Maybe you don't need one. You maybe running efficient speakers and the power section of your AVR might be doing a good enough job, for you.
I would not conclude that this is the approach one must take to decide whether one needs an external power amplifier or not. That is not right.