The simple answer is no, the word Gregorian isn't mentioned in the text of The Urantia Book, but the authors do use the Gregorian calendar for their date references.
There are 6 references to the year 1934: (31:10.1), (56:10.2) , (62:5.1) , (62:7.6) , (63:6.7), (74:0.1), And one for the year 1935 (119:8.9).
The year 1934 is used as the base year in the precise date calculations given by the authors of the papers, 1934 being the year when the bulk of material was indited for Parts I-III; the restatement of Jesus' life and teachings came after that in 1935. The specific dates of Jesus' life begin at 7 B.C. The dates A.D. are based on the Gregorian calendar. B.C.dates prior to Jesus are usually counted back from the year 1934.