No. A national trademark registered in an EU member state cannot be converted or extended into an EU trademark. The EUIPO conducts its own examination; an application must be filed directly with the EUIPO and assessed on its own merits.
However, if your EUIPO trademark application is refused, you can still refile it as multiple applications in each individual member state, excluding the one jurisdiction where the refusal happened. In other words, an EUIPO application can be converted into individual filings, preserving the original EU filing date. This conversion mechanism exists to protect applicants whose marks are refused in one or more member states.