I migrated to gmusicbrowser in 2017. Before that, I used Songbird, since about 2013. From 2013 to 2017, I have playlists indicating what month a song was added. However, gmusicbrowser shows them all as being added in January 2017.

My question is whether I can trick gmusicbrowser into thinking these songs were added before they actually were. This would make it easier for me to use smart playlists and weighted random.

There is no easy (via gui) way to do it, but you can either edit the gmbrc file with a script, each song is one line, fields are tab separated, dates are in unix time (seconds since epoch). Otherwise I can give you a command-line that sets the date for a song, still needs a script though.
If you don't know how to make the script I can help you, just give me an example of your playlist that contains the dates.