If there are no localized observables in quantum gravity, does spacetime really exist, or might spacetime really be an illusion?
Andrew Strominger thinks spacetime is an illusion. It's all a Cosmic Hologram at the future boundary of spacetime at the end of time. It projects out the illusion we see around us.
I think this question is a bit too broad, as it depends on the theory you're talking about.
Strangely, Lubos Motl has just posted a new article about (a similar to tthis) idea..
Well, you do have spacetime in string theory, for example. But as Lubos Motl mentions in the article linked, the metric tensor isn't exactly that well-defined at the stringy scales. To qyuote the article:
Sam#e with things like Twi#stor theory (I think, correct me if I'm wrong.); the real space is the space of twistors.