I think there will be errors but not in the build time. It is likely issues will happen in the run time. You won't be able to access file systems on the client side just like how you can't access the window object on the server-side.
In my current project, we have utility functions for both the server-side, client-side, or universal. All server-side functions are called in getServerSideProps to make sure they work as expected. All your server-side code in getServerSideProps will not be imported as part of the client-side bundle if that's what you mean by "dead code". According to the Next.js
Note: You can import modules in top-level scope for use in
getServerSideProps. Imports used in getServerSideProps will not be
bundled for the client-side.
This means you can write server-side code directly in
getServerSideProps. This includes reading from the filesystem or a
database.
I'm not aware of a way you can ask webpack to bundle part of the file or execute a subset of import statements.
I hope that provides some help.
Reference:
Docs - getServerSideProps
Custom Webpack Config