I tested again and the max CPU usage once the app has been backgrounded is .85% for 1s. The rest of the time the usage stays at 0% (see screenshot). For scenarios when I continually open the app and close it, the max is about 10%, but it gets back to 0 once it's backgrounded or when no longer in use.
I would not attribute this amount of CPU consumption as a cause for battery drain. There are far many other factors, including networking, which is the greatest factor for power drain.
I understand you are concerned about the performance of your app, but so far in my testing all I have seen can be accounted for. I recommend profiling your app using
Systrace, so you can look into how your app is doing frame by frame.
Here is a trace I did just now.
The trace was for 10 seconds, during which I launched our sample app, let it load the banner, and backgrounded it at the 5th second. The remaining 5 seconds was purely no work app-wise. Looking at the trace, you can see all 8 cores of my Nexus 6P turned on from the beginning up until 5.5s, that was when I hit the home button to background the app. A bit more work there for handling that input event, but after that towards 10s you can see more than half of my cores have turned off. At the end, only two cores were still churning out some calculations.