Qualified yes, but it becomes more difficult (and impossible depending on the functionalities required)
Devices with Google Play have a set of integrated services – Google Play services – provided for free (or almost) apps. These services include Location & Maps, push messaging (formerly Google Cloud Messaging, now Firebase Cloud Messaging), Google Sign-in, and more. These services offer developer lockout because they are available on any device that comes with Google Play Store.
All of these services are subject to change over the course of their lives and Google has already announced that APIs 14 and 15 of the Google Play services for Ice Cream Sandwich (ICS) will no longer be updated.
This means that for any app developer interested in the current market for Android devices with Google Play services, they will need to do extra work to support older devices where Google's APIs are frozen.
Another problem for developers is that the version of WebView prior to Android 5.0 was related to operating system updates. The problems / peculiarities of WebView varied depending on the manufacturer and the version of the operating system.
You should also look for old web browsers because Firefox and Chrome are running Android 4.0 or higher. For example, advances in mobile website development may occur on older browsers.
What can I do
Run a custom ROM with a replacement for Google Services if needed, see: Fakestore, blankstore, gms, microg, unifiednlp – what's better for Android without Gapps?
What if I do not want root / custom ROM
Any developer should find corresponding APIs for Google services, which would work with the lower API of the device. They will probably have to pay for free services with Google services, such as map mosaics embedded in the app and push notifications.
Note that even the F-Droid open source application store now has a minimum level of 14 APIs, Ice Cream Sandwich
Developers are always free to create applications that users can download and load laterally on older devices, if they do not use outdated Google services for this device.