I'm a little concerned about your level of understanding regarding FSMA and certification. Your PCQI should know that there is no such thing as FSMA certification. If your PCQI does not know that, I think I would suggest additional training.
Bottom line is you can claim that your company is FSMA compliant but unless you've had an audit, you have no evidence to back that up. If a buyer asks you can show them a PCQI certificate and Food Safety Plan and see if they accept it. Most retailers will not.
I think 3rd party audits are good for making sure you're staying on top of your requirements and would recommend scheduling one, regardless of what your current customer accepts.