Yes, you can, or you could use something else.
First, a little background information. MicroG comes with two replacements for the Play Store. FakeStore is an app that fakes the existence of the Play Store to make apps happy but provides no actual store implementation. BlankStore provides a partial implementation for downloading free apps but does not support paid apps, paying for apps, or validating purchases. Only the official Play Store allows for that, and it does work with microG. If you are worried about privacy, however, you may want to severely limit its permissions - does your app store really need access to your text messages?
Before getting to how you can install the Play Store, note that you can find a list of alternative app stores in the No Gapps setup guide. You could, for instance, use the app Yalp Store for apps and have FakeStore installed just make apps think the Play Store is installed.
There are a couple of caveats to using the official Play Store. First, it works best when installed to
/system/priv-app and not as a user app. Second, every so often when the Play Store is opened (usually the first time after rebooting), it will only display a blank screen. To fix this, all that needs to be done is to completely close out of the app - this means removing it from recents, not just hitting the home key - and open it back up again. It should work on the second try.
The easiest way to install the Play Store is to use the flashable zip file from the downloads section which installs only the Play Store to
/system/priv-app so you can install microG as a user app. If you are running Nougat, you can use the bundled zip instead that contains both microG and the Play Store.