Qualcomm is also American.
Whether Intel sells or not is decided by its major shareholders, pending regulatory approval, not Intel's execs or employees. Those shareholders would likely receive shares of Qualcomm which would now include Intel's expected future profits, or cash that they can use to buy Qualcomm shares to capture those profits.
Then Qualcomm would become a national security asset. ๐ In fact that alone sounds like a great reason for acquisition. It's not every day that you get a obvious way to become too big/important to fail.