Android - Can I delete an app I got on sale?

From play store support:

You can use apps you bought on Google Play on any Android device without paying again. However, each device must have the same Google Account on it.

You can:

• Reinstall an app you bought but deleted
• Install an app on more than one Android device.
• Install an app on a new Android device.

Even though the app you downloaded was free now, being that usually it is a paid app, Google will count it as if you paid $0.00 and therefore it's counted as if you bought it. And as quoted above, purchased apps can be reinstalled later.

Bochur's answer is correct. By way of additional information in your Play Store → Account → Order History , these apps will be shown as 0 price payment apps as the screenshot below shows - all these apps (barring third) were bought free (discounted) and I can install them again on any device (of course with the same account)