As long as Intel is still an operating company, and near monopoly in client, the government is not going to approve merging it into another near monopoly (QCOM).
I think the only way this could be approved is if Intel was about to go under.
Intel has a near monopoly in PC client, and Qualcomm has almost no share in PC client. Qualcomm's monopoly in is cellular modems/chipsets, where Intel has zero share. They don't care so much about two monopolies merging if they are monopolies in separate domains, so long as the monopoly in one can't be leveraged to maintain/increase the monopoly in the other.
I don't see how Qualcomm taking over Intel's PC business would hurt the competitiveness of the PC industry (ARM PCs will still be able to be made by Nvidia, Mediatek, etc.) or help their monopoly in cellular modems or Android SoCs.
I don't think this would be good for consumers, but it wouldn't be bad. It isn't as though Intel hasn't acted like a monopolist, and the government would have to chase to leash them to some extent by putting conditions on the merger that would seek to improve competition. Maybe they'd be required to spin off their ARM design efforts if they wanted to take over Intel's x86 design. Maybe they'd be barred from integrating cellular modems into their PC chips for a period of years (not that I think that could ever be a successful market, but just in case) Maybe they'd be barred from offering x86 SoCs for Android (another "just in case" to prevent them from owning some sort of hypothetical x86 Windows "Dex" type market)