It used to be. I found this more in-depth explanation of why NSW switched to the current SQT format.
Following BUD/S training, graduates remain attached to the NSWC in Coronado while they complete a secondary training program currently known as SEAL Qualification Training (SQT). During the first decade and a half of the SEAL Team's existence that secondary training was actually conducted under the direction of the SEAL Team to which a man had been assigned upon completing training. After a new BUD/S graduate reported to the SEAL Team he underwent additional training which lasted approximately six months. During that time period the new man was "on probation" and did not officially hold full SEAL credentials. At the end of that supplemental training program and period of probation, the new man was evaluated by his superiors. If deemed physically and mentally suited for SEAL Team duty and if he had successfully completed all of the secondary training program, the new man was officially granted SEAL status. An entry was made in his Personnel Record designating him as a "COMBATANT SWIMMER (SEAL)" and his Naval Enlisted Classification (NEC) code was changed to reflect that new status. At that point he was a fully-credentialed Navy SEAL.
The 'old way' of handling secondary training caused new BUD/S graduates to be listed on the manpower roster of the SEAL Team, but prevented them being utilized by that Team until they had successfully completed the full secondary training program, and the probation period. The SEAL Team manpower roster may have been full, but not all of the men listed there could be deployed as fully-trained SEALs. This handicapped the SEAL Teams and effectively left them shorthanded, despite a full manpower roster. To remedy this situation, the secondary training effort was relocated to the Naval Special Warfare Center (where BUD/S is conducted). The new BUD/S graduates would now complete their secondary training and probation period, and became fully-credentialed SEALs before ever being assigned to a SEAL Team. This meant that every man assigned to a SEAL Team was fully qualified and could be utilized by the command without waiting.