is it true that RR scaled up Merlin/Gryphon superchargers to make the centrifugal compressor stages of their early jet engines
The short answer is no. Also, tis Griffon rather than Gryphon.
Whittle’s original patent (16 March 1930) shows a compressor of 2 axial stages followed by a centrifugal stage but he subsequently only used a double-sided centrifugal compressor because of its greater simplicity (as had von Ohain) and because British companies had more knowledge and experience with this type, from their use in piston engine superchargers. With so much else that was new, risks had to be reduced where possible. In practice, early German axial engines suffered more than centrifugals from poor acceleration, vibration, compressor surge and blade stall problems, although ultimately axial compressors would prove the way to greater power and efficiency.
Contemporary superchargers were capable of 2.5:1 compression ratios at 65% efficiency. Whittle required 4:1 ratio at 80%, which required 3,000 horsepower from the turbine, and at 16,000 RPM. By contrast the Merlin two stage supercharger consumed only 400 horsepower.
The Welland was actually designed by Frank Whittles team at Power Jets, and meant to be put into production by Rover as the W.2B/23. Rover were having trouble producing parts and RR were called in to supply the required items. Rover continued to have troubles and production was taken over by RR. RR incorporated the best features of Whittles W2/500 and the Rover B.26 into a new design, called the B.27 or Derwent. Stanley Hooker of RR was their supercharger expert and there is no doubt that his expertise was brought to bear once RR took over, but RR can not lay claim for the centrifugal compressor in the early jets. The Nene (the Tay was an afterburning version - not to be confused with the 1987 Tay) was a development of the Welland and Derwent and the last of RR's centrifugal jets, the Avon being the next which was axial.