Apple uses their own SoC with a Qualcomm modem so I don't see why Google couldn't do the same. It would probably cost more than Snapdragon though.
Google doesn't have nearly the same leverage and volume numbers to use against Qualcomm as Apple does, but even for Apple it's a devil's bargain. The licensing terms are incredibly onerous. If they updated them and you didn't agree, they used to just cut off your entire company's chip supply until that was ruled monopolistic and illegal. The royalties (one of the only royalties Apple actually pays) are substantial percentages of the final device price. Getting into bed with Qualcomm needs to be weighed against the risk to the rest of your business.
As a consumer, I buy Qualcomm modem phones, but as an engineer Qualcomm is only marginally below the plague on my avoidance list.