In the old days I would have been scared to replace the controller. Not because of drivers, but because uncertainty of compatibility – would both controllers support the array metadata that is on the drives? (If the new controller does not, it can’t assemble the array.) That side of things has improved.
In principle one could look up the device ID but most trivial method is by lspci and then the controller has to be plugged into some machine. Not necessarily any drives connected though; just to see the ID and whether there is driver support. Then install the driver to system before replacing controller.
The initramfs is a filesystem in a file. The bootloader loads the kernel and initramfs. Kernel uses files (drivers) to find devices and activate them so that it can mount the / filesystem.
The installer’s initramfs has all drivers (that are included in the distro). It is fat. That way the installer can run on all (supported) hardware.
The initramfs of an installed kernel has only the necessary drivers in it. “Lean and mean”. It is possible to tell the dracut to include “unnecessary drivers”, when you run it explicitly. That way you can inject the controller’s driver before you have one on the system.
Would I have done that preparation? Probably not. An “oh hell, lets just try” followed by solving the inevitable mess, while not wise, looks the likely path.