In his monograph on the
Argyrotype process, Mike Ware states that prolonged washing in the fix can lead to loss of density in the highlights, so a rapid fixer may be too aggressive for the fine silver particles in the image.
Also, if the TF-4 is on the alkaline side of neutral pH, there is the possibility of residual iron being left in the print. A problem that the Argyrotype process had been designed to prevent, as residual iron(III) can oxidise the silver causing image degradation.
That is not to say you shouldn't try it, just keep the potential problems in mind.