In a nutshell it is going to affect things, which has configuration specific to the current theme. Out of native functionality that would be most prominently:
- menus (which are assigned to theme locations)
- widgets (which are assigned to sidebars)
This can go further if theme provides sidebars and custom widgets for example.
Overall there are rarely major issues with switching themes, but there can be plenty of configuration inconvenience, depending on specifics of the site.
Professional developers pretty much exclusively do any development/testing on separate copy of site (usually using local development environment on their computer).