Due to the recent Play Store changes you can no longer "add text or images that indicate store performance or ranking, or suggest relations to existing Google Play programs in the app title" [1].
You can't, for example, add "#1", "best" or "free". However, you can't also add "no ads".
To be precise: appending "[small, no ads]", "[no ads]" or "[without ads]" to the play store app title causes a rejection. I didn't want to test more in fear of banning, and in the end removed it.
I know you can see if an app contains ads in the app page, but not in the search results... or at least not yet, but I doubt Google will add that indication.
[1] https://support.google.com/googleplay/android-developer/answ...
For those who aren’t aware, in the games industry the distributor has been in the role of adding DRM to games on the pretense that they are “protecting their interests and channels”. As the distributor, Google may feel empowered to make these sort of “protective” changes, and the one that would be most likely (in my estimation) would be wrapping the APK such that it played a pre-roll ad before your free game started.
I could be completely off base here but to my way of thinking it would be consistent with Google’s moves in the past.