Yes, it does work. I just verified it. I'm using BR 4.2, but TRACE PRINT has been around forever.
LOAD PROGRAM
RUN TRACE PRINT >tracefilename
When the program exits, the file is there. TRACE PRINT (without the redirection to a file) was originally designed to print directly to a printer (it still works too). But wastes a lot of paper so I don't do that generally.