STPP doesn't produce suds on its own.
It does soften water, and soft water suds more readily than hard water, although modern synthetic surfactants are not very affected by hard water in this respect. STPP certainly would help natural soap suds better, though.
By pre-mixing STPP with the detergent, and then using the same amount of the mix that one might use of the unadulterated product, the surfactant concentration will be reduced and sudsing may well be reduced as well.
I work with machine tools that use a water based oil/coolant. The coolant splashes about and my work clothes usually get some. Not soaked, but enough. The coolant also contains an industrial strength foam suppressant and I've noticed that my work clothes typically don't suds up much in the washer, even if I add twice as much detergent-stpp mix as I would for a lightly soiled load. It does give me an excuse to use a high sudsing Mexican detergent for the work duds, though.