Apparently not. From "The Origins of PostScript" mentioned by GP:
> The architecture suggested by John Gaffney was to be based on a fictitious stack machine (at that time we had no knowledge of a similar approach taken by the Forth language).
That is the only mention of "Forth".
Honestly, my first curiosity regards whether Chuck Moore and Forth get any mention or whether this is a true parallel development, possibly necessitated by the hardware at hand. My perception, based on zero evidence, was that Forth had some influence on the design of Postscript.