I picked up & drove my car back from i25 Kia in Colorado to the Bay Area last week and just got it registered today, so I can share some details on the registration process from my end. I had a descent gap in-between the purchase date and actual date of entry to CA so might be interesting case to some.
You can check my signature on the exact dates, but when I ordered my vehicle and got my first ETA from the dealership, I was given late November (11/23) so I went ahead and booked a flight early December to avoid the holiday pricing on airfares. Turns out the vehicle arrived to the dealership way earlier than expected (11/5), but I checked the DMV website regarding
registering out-of-state vehicle and
when exactly fees are due and noted (like everyone else is mentioning) that as long as I register within 20 days from when I entered CA, it should be good so I wasn't too worried.
Since I started the documentation early, I already completed all my documents by early November and waited about a month to fly over. I then drove the vehicle back to CA through i80 route last week (first week of December; luckily, it's been a warm winter year for CO/WY/UT/NV so no snow at all).
I made the trip back in 2 days, got the smog check completed yesterday and registered today at my local DMV where my dealership sent the documentation to. Pretty smooth process overall - just make sure to smog check, line up to the vehicle inspection line first before going inside, and bring your checkbook + any other documents noted on DMV.
TL;DR as long as on your REG343 form you mention when you enter CA (for me it was beginning of the month), you shouldn't be penalized, even if there's some gap between purchase date and date of entry to CA.
As for the temp plate from CO, similarly to SLPV's case, DMV did not take my temporary CO plate either. Cheers