Not only the play store is needed. You need to install an special package with the whole of Google services, often while in recovery/download mode.

But, to answer/illustrate your question, as a matter of fact, you can install Play store apps even without Play store. Aurora store is an app that connects to the Google servers too get you the very same apks. That's when you realize, after installed the banking app, that it starts bitching about the Google services missing. "This app was designed to run with Google Play Services, and cannot operate without it". And poof, it auto closes in your face.