In CS, types are usually a higher level of abstraction built on top of more fundamental layers. If you choose to break the abstraction, you can definitely use an integer as a string, a list, or a function. The outcome is unlikely to be useful, unless your construct was designed with such hacks in mind.

When I did a PhD in theoretical computer science, type theory felt like one niche topic among many. It was certainly of interest to some subfield, but most people didn't find it particularly relevant to the kind of TCS they were doing.