Can a Data Scientist Become a Software Engineer?

Is this a trick question? A data scientist can become a software engineer and a software engineer can become a data scientist. Both involve compute and data structures in different domains, with a different set of tools and frameworks.

Formally, I would think if a data scientist wanted a more formal CS education, one would take an intro to OOP class (just take a basic Java or C++ tutorial or something to learn about data types and some OOP), algorithms and data structures, operating systems, computer architecture, and networking. Akin to how if a software engineer wanted to become a data scientist, one would take linear algebra, calculus (to understand back propagation and minimizing some error function), machine learning, and perhaps some data science specific sources like data cleanup with canonical DS tools.