No, that is not correct. The two seated night fighters were all converted from single seat to two seat night fighter configuration by Deutche Lufthansa works at Staken near Berlin. There has been a lot of confusion about this, two seated trainer aircrafts fitted with radar to become night fighters.
The fact is, that the only component shared between the trainer and the night fighter was the 400 l rear main fuel tank under the rear cockpit. The rear cockpit of the night fighter are compleatly different to the trainer and NONE trainers were converted into night fighters.
So Red 8 was "born" as a nightfighter in early April 1945 as one of only 7 aircrafts in build as night fighters.