Yes, but with the caveat that your version 31 program cannot be using an capabilities that a version 20 controller does not have. Also, it isn't as straightforward as downgrading to a more recent version. More on that further down.
First, open your version 31 file and do a Save As and change the format from .ACD to .L5K and save the file. This will create the export file we will have to manually modify to make it compatible with version 20. Open the .L5K file in a text editor. Notepad is fine. Scroll down to Line 12 where you should see the line containing IE_VER := 2.22. Change the number there to 2.11.
Next, search through the document for "CHILD_PROGRAMS". When you locate it, look below it for "END_CHILD_PROGRAMS". If there is nothing between those two lines, then you are not using child programs. Delete those two lines. These were added starting in version 24 and are incompatible with version 20. Save the modified file. Child Programs is a feature of the Logical Organizer and how Programs are arranged on that display. If you do not require this, you could delete the lines between CHILD_PROGRAMS and END_CHILD_PROGRAMS. It would then revert to the default method to display the Programs.
Go back to your Logix software and select File, then Open and browse to the L5K file you modified. Select it and click Open. You will see a Save Imported Project As window open. Type in a different file name so you do not overwrite your original project. Then you MUST change the Revision field to Version 20. Then click Import.
The Import will take a minute before it appears to be doing anything. That is normal. Then after a moment you should see RSLogix 5000 open and if it was successful, your application will be ready. If there were any issues, scroll up in the Error window and note the Line number for any errors. Don't worry about warnings. Only errors will prevent the import. That Error line number is the line number in the L5K file. Go back to your text editor and review that line to determine what the error might be.
Good luck!
OG