The answer is likely YES and it doesn't matter whether filed together or separately:
The State of California says at
https://www.ftb.ca.gov/individuals/treasury-offset.shtml
Treasury Offset Program
If you have a past-due, legally enforceable California income
tax debt and are entitled to a federal income tax refund, the Franchise
Tax Board (FTB) is authorized to offset that refund and apply it
toward your balance due. This may result in an additional offset fee.
The Bureau of Fiscal Services (BFS), a bureau of the U.S. Department of
Treasury, administers this Treasury Offset Program.
We will send FTB 1102PC, Intent to Offset Federal Payments, by
certified mail to your last known address. The letter explains that we
plan to notify BFS of the debt if you do not pay in full within 60
days.
We continue to pursue federal offset activity even if you are in an
installment agreement. We will also offset any California income tax
refund until your debt is paid in full. BFS will send you a
notification explaining why your federal refund was reduced, and that it
may take several weeks before the federal refund reaches FTB. They
will also send any remaining federal refund amount to you.
BFS will send you a notification explaining why your federal refund
was reduced, and that it may take several weeks before the federal
refund reaches FTB. They will also send any remaining federal refund
amount to you.
To avoid the offset, you must take one of the actions below within 60 days from the date of the certified letter:
Pay the debt in full
Pay the full amount listed on FTB 1102PC, Intent to Offset
Federal Payments. Use the payment coupon included in the letter when you
send your check or money order. You may also pay online.
Request a review
If you believe that all or part of the debt is not past due or
not legally enforceable, you must send evidence to support your
position. Send your evidence to:
STATE OF CALIFORNIA
OFFSET PROGRAM MS A141
FRANCHISE TAX BOARD
PO BOX 2966
RANCHO CORDOVA CA 95741-2966
Bankruptcy
If you filed for bankruptcy, contact us one of the following ways:
Provide us with your bankruptcy case number and the name of the
bankruptcy court. Although you are not subject to offset of your federal
income tax refund while the bankruptcy “automatic stay” is in effect,
you still are obligated to file tax returns.
Native Americans
If you are an enrolled member of an Indian tribe, and you
believe your income is not taxable, you must send a letter explaining
why. Send your explanation to:
STATE OF CALIFORNIA
OFFSET PROGRAM MS A141
FRANCHISE TAX BOARD
PO BOX 2966
RANCHO CORDOVA CA 95741-2966
There are reports that the FTB hasn't always followed its own rules:
https://klasing-associates.com/cbs-reports-california-ftb-improperly-seizing-income-tax-refunds/
so be sure to check that you have received the require notice(s).
