With the Birdy 3 tensionner, there is no need to do anything like pulling the chain, just folding the rear swing arm, same as when folding the rear triangle of a Brompton with the Brompton chain tensionner.

The only difference with a Birdy with a cassette+derailleur is that the chain must be placed on the smallest cog to be able to fully fold the rear swing arm but this has nothing to do with the chain tensionner.

It seems that you are in Paris, if its the case why not test the folding of a Birdy Touring or Rohloff with this tensionner at Les Vélos Parisiens and decide if its worth its price?