They certainly can consider that your daughter has less need because she is now getting a Cal Grant.
Say that your EFC is $20k but the cost of the school is $70k. The school is going to try to get you close to that $20k number.
Cal Grant - $9k
Fed Loan - $5.5
school grant - $20k less $9k less $5.5 = $4.5k
That totals $20k. Some schools will meet the ‘need’ without loans so may leave the school grant at the offer of $10k (your example) or even increase it to $11k. The school may also give you opportunities to pay the difference with parent loans, work study, other scholarships (talent like music or theater, art).
Most schools do not meet full need for all students. They may be more generous than just meeting your EFC, but are still a long way from covering all costs.
But can schools consider that you are getting the Cal Grant when awarding your school aid? Yes. Also can consider outside scholarships, federal aid, and reduce their aid.
We have a couple of very generous scholarships programs in our state. If a student wins one of these (full COA), the schools definitely withdraw their own aid that may already have been awarded, and even the tiny per credit state award is removed from the tuition bill.
Financial aid is a lot of moving parts.