Writing an app as a proof of concept just for fun may be doable, depending on what you already know, how good you are at learning, and how much time you want to invest.
Writing an app that's better than the several existing apps? Definitely not.
Edit: looking at the text - go for it (if you want it primarily as a learning experience). The network stuff certainly will have some new concepts (especially around logging in) but it's not super complicated. You'll basically end up having a function "getComments" that sends a HTTP request (calling a library) and converts the JSON response into your internal data structures.