The short answer is yes. Under the Florida Rules of Criminal Procedure, you may ask a Court to seal - not expunge - a record even if FDLE denies you a Certificate of Eligibility.
A Certificate of Eligibility is required for a non-judicial (records beyond the court file) by Florida statute. The criminal rules, however, do not require a Certificate of Eligibility to seal a judicial record (court file).
While it is rare for judges to grant Petitions To Seal without an FDLE Certificate, it is important to remember that for a judicial record sealing - just the actual court file, not police or non-judicial records - the Court is well within their right to seal their own record, even if you have a prior expungement/sealing or a conviction that prevents you from being able to obtain an FDLE Certificate.
Talk to your Florida expungement lawyer about this process if you are not otherwise eligible to apply for a Sealing or Expungement through the Florida Department of Law Enforcement.