Can developers build applications for unsupported Android versions?
You are free to build any app for unsupported versions of Android. However, you won't be able to publish on Google Play Store (if you intend to).

From an article published when Google ended support for ICS:


  First, Google won’t allow developers to publish apps that support the API level for ICS — that’s API 14 and 15. That means the oldest supported version of Android in the Play Store is Android 4.1 Jelly Bean (API 16).