Can 32-bit assembly code be ran on a 64-bit processor? (Delphi)

Can 32-bit assembly code be ran on a 64-bit processor? (Delphi)

I am writing a program in Delphi, and including a library which contains
some assembly code (Pipes.pas). I am getting an access violation when I
run the code which makes a call to a function called StdWndProc. The
process is an assembly function which contains assembly code.
A while back I updated this code (Pipes.pas) to include unicode support
and other stuff, but I didn't figure out what this assembly was doing. Any
ideas on what's going wrong here?
I'm running on a 64-bit machine, could it be that this assembly is 32-bit
and isn't running correctly on a 64-bit processor (the project is targeted
at 32-bit build).