The answer is yes, you can make a functional DIY smart phone powered by a Raspberry Pi. Here’s more from Hackaday:

[asherdundas], the phone’s creator, actually found a prior build based around the Raspberry Pi before starting this one. The problem was that it was built nearly a decade ago, and hadn’t been updated since. This build brings some modernization to the antiquated Pi phone, and starts with a 3D printed case. It also houses a touchscreen and a GSM antenna to connect to the cell network. With some other odds and ends, like a speaker and microphone, plus a battery and the software to tie it all together, a modern functional Raspberry Pi phone was created, with some extra details available on the project page.

The phone has the expected features — including calling, texting, and even a camera. A small WiFi USB dongle allows it to connect to the Internet too, allowing it to do all of the internet browsing a modern smartphone might want to do. The only thing that it might be pretty difficult to do is install Android apps, and although there are ways to get Android apps working in Linux, it’s not always strictly necessary to have this functionality.

See project!