So I'm not a lawyer, and I'd like to believe what you've written here, but I don't think what you've said is correct from a reading of the California vehicle code. Not trying to be picky but it is a confusing area and I think it's good for the facts to be out there.
My understanding is basically that:
You must have a license issued under the California Vehicle Code to drive in California, unless you have an exemption. See 12500(a): https://leginfo.legislature.ca.gov/faces/codes_displaySection.xhtml?lawCode=VEH§ionNum=12500.
One exemption to the above is that you are a non-resident of California, holding a valid foreign-issued license. See 12502(a)(1): https://leginfo.legislature.ca.gov/faces/codes_displaySection.xhtml?lawCode=VEH§ionNum=12502.
If you are driving in CA on a foreign license under an exemption, such as a non-resident using a foreign license (12502(a)), and you then become a resident, you may continue to operate a motor vehicle in CA under that excemption for a max of 10 days. See 12500(c): https://leginfo.legislature.ca.gov/faces/codes_displaySection.xhtml?lawCode=VEH§ionNum=12505.
So from a legal point of view it seems (unfortunately) pretty clear to me actually. You are exempt from the requirement to have a CA license if you are a non-resident with a valid foreign license. Once you become a resident, that exemption expires after 10 days and my reading of that is your foreign license is thus no longer legally valid in CA.
Whether it's practical or sensible law in the scenario we're talking about, or whether it would be likely to be enforced if an individual could demonstrate they had taken all practical steps to obtain the license as quickly as possible, is of course up for debate but won't be solved on here. There is also the question of course as to when a new arrival becomes a resident, but all else equal I think crossing the border on an immigrant visa and travelling to a spouse's abode with the intent of living there will count.
I do think it's unreasonable that there isn't some kind of grace period for new arrivals who have other barriers such as SSN and just the lack of DMV availability within 10 days, especially for the drivers test, but so it goes...