I've done enough tests that I have some real numbers. This was done on my Galaxy Stellar, since the results (to my eyes) were more noticeable than on my Nexus 7.
I tested from a fresh reboot. Start [app], time. Force stop [app]. Repeat 4 more times. Take average.
Chrome (to bookmarks page):
Without patch: 2.1 sec
With patch: 1.4 sec
Maps (to showing my location with full map draw):
Without patch: 4.2 sec
With patch 3.1: sec
Google+ (to main page with full picture rendering):
Without patch: 3.5 sec
With patch: 2.2 sec
Bible (YouVersion) (to current passage):
Without patch: 6.3 sec
With patch: 6.5 sec
I didn't see anything near 4 or 5 times faster, but the speed increases were definitely noticeable on some of the apps. Oddly, the Bible app was actually .2 seconds slower on average. Probably no difference at all.
I also did a few framerate tests, and all came within a few fps of each other with no benefit one way or the other. It doesn't appear to help framerates at all.
So, not totally a placebo effect, but some of the benefits people are claiming I wasn't able to back up on my hardware. That said, there could be differences in hardware that aren't accounted for here. More people just need to test and give real numbers.
Edit: I haven't noticed anything significant as far as battery life goes. I just switched from m-kernel a25 to a26, so it would be hard for me to separate the difference and I don't feel like taking the time to get real numbers on this. Just the fact that I haven't noticed a problem makes me happy enough.
Also, I didn't use the APK; I flashed the zip that was linked earlier which contains an init script to start it up. Don't know if that makes a difference, or not.