Matt Ridley, writing in the Wall St Journal today says "No it doesn't." As a retired engineer, who spent forty years gainfully employed in private industry, doing R&D, I can relate to this. I created, either in part or in whole, an medical ultrasonic imager, a portable Holter monitor, a data acquisition system running off an IBM PC, a digital oscilloscope, a cardiac Xray system, a video compression chip, and an overfill protection system for fuel tank trucks. All of 'em privately funded, half of 'em made it to market. Government funding is not required for technological advance. Nor was basic scientific research in to basic scientific principles needed. In fact, the one time I picked up some basic research from a scientific journal for a project, it turned out to be wrong, it worked, but at only one half the performance claimed in the journal article. I looked up the author and telephoned him. After a lengthy conversation, the author admitted that yes, he had exaggerated his claims a little bit.
On the other hand, during the existential struggle that was World War II, government funded R&D produced nuclear weapons, jet aircraft, radar, airborne magnetometers, proximity fuses, handheld two way voice radios, and effective back pack anti tank weapons. In the following Cold War, government funded projects took us to the Moon and launched the Internet.
Much university research is funded by government grants. On the other hand you have all seen the video of a shrimp on a treadmill, government funded all the way. As long as corporations are allowed to deduct R&D expenses for tax purposes, progress will be made.