Most of the SDK has been tested and confirmed to be fully functional on real hardware, but there is some copy protection you will have to get around in order to run arbitrary software on a PS1. The traditional solution is to perform disc swapping or install a modchip, but nowadays we also have softmods [1] that make the process as easy as inserting a specially formatted memory card (which can be prepared using a PS2, or even a PS1 by swapping discs).
You are not required to use CDs either. With the help of some code and linker script magic, you can build an image that can be booted directly from a cheat cartridge (or simply a parallel EEPROM) connected to the console's expansion bus, bypassing the copy protection checks entirely. There are also debugging tools that, once loaded, let you download an executable into RAM for quick testing and manage memory cards using a modified serial cable [2].
[1] https://github.com/brad-lin/FreePSXBoot
[2] https://schnappy.xyz/?building_a_serial_psx_cable
