Your refund will not necessarily be delayed by claiming the $600 stimulus.
If you had not received $600 for the second stimulus payment, it must be reported on your tax return in the Recovery Rebate Credit section.
If it has been more than 21 days since you filed, then there may be some other reason for the delay.
For more information from the IRS about what can be done while you are waiting, see: Tax Season Refund Frequently Asked Questions.