No, it isn't. It's well established that normally, when someone dies in KH universe, their heart joins Kingdom Hearts, which is roughly equivalent to the concept of World Soul in Hinduism and Buddhism. That means, they cease to exist as an individual. However, there are exceptions for this rule. Some worlds have a form of afterlife specific to them. So far we have seen two of these, Underworld in Olympus and Davy Jones' Locker in Caribbean.
The official translation of UX is very unclear (or censored) about this, but from the unofficial one we can see that the Master of Masters wanted to avoid wasting a large number of lives in the Keyblade War. I don't think he created Quadratum (he said it is too strange even for him to understand), but he discovered its existence and connected it to KG to function as its world specific form of afterlife, so the people who died in the war would end up there.
Now, let's consider all the people we know are in Quadratum:
- From Yen Sid at the end of Melody of Memory we know that "Ancient Masters", which must refer to the foretellers, went there. They died in the Keyblade War in KG.
- Sora disappeared from Destiny Islands, but the breaking of the laws of nature that resulted in his disappearance happened in KG. In that sense he sealed his fate there.
- The last time we saw Luxord, he was dying in the KG. We assumed that he would be recompleted, but if that failed to happen for some reason, then he would have ended up in Quadratum.
- For Strelitzia, we don't know for sure. There seem to be two possibilities. First, it's possible that the ark/lifeboat can transport people directly to Quadratum, and Luxu simply sent her there with it. Second, she could have been sent into the future just like the others, landed in some world (which must have been KG for this theory to work), and then there wasn't anyone there to summon her body back. I would assume that after some time in limbo, she became dead again.