The idea of parallel timelines subjective to time-travel more or less opens infinite possibilities. it is a wild guess that no, it would not erase or rewrite it. It might in our imagination, but for the time being, it did not. As a matter of a fact, we don't even know what results once Serge awakens.
As for "Everything was just a dream/imagination" type of endings, I'd rather spill my brain out than see it end that way as it would be the utter incarnation of absolute idiotism...(personally, I wish I'd see a sequel to Chrono Cross, but I so much fear they'd use completely new characters, and without any magicka Chrono had, following the FF downfall, that I rather just enjoy CC all over again, and keep them present that way. I don't even support the fanbased work. If you ain't the Chrono Cross staff, you can't make it, and therefore, don't even try. That about sums it upfrom my point of view. as a matter of a fact, Chrono Cross doesn't need a sequel...)
