This has been discussed before and seems to be a widely contested topic on the Nexus, with no final answers. Here are some pertinent links:
With that out of the way, I will say that I think it really depends on what you personally consider as "real." As an epistemological solipsist, I think it is an unresolvable question, at least at this time, if anything at all even exists outside of our own minds. I'm not saying that it's not there, just that it's truly impossible to know anything for sure other than the fact that your being exists.
However, if you believe in the shared consciousness ideal that so, so many Nexians and psychedelic users abide by, then you can start to make headway with the idea of objective reality or objects outside of anyone's mind. For even if I can only know my true consciousness, if my awareness and your awareness are actually one-and-the-same, then something that we can both sense becomes real in a way that's more objective than the general unified subjectivity that we seem to share on a day-to-day basis.
So for the rest of this post, let's assume that we do derive our beings from the same ultimate source. If this is the case, then confronting the idea of hyperspace poses even more questions. If we all exist as a collective consciousness, can there be anything else? Does this collectivity create the universe, or the other way around, or do they just happen to exist simultaneously?
Is there an origin of consciousness, or is it something that has always been around? Do extraterrestrials, or even animals and bacteria, share in the same source as humans? When we travel to hyperspace, are we simply accessing a higher realm of our shared being, or a new plane entirely?
Since we cannot really be sure of objective existence outside of our minds at this time, it is very hard if not impossible to answer these questions. The best thing I can recommend is to explore more and push deeper and deeper into hyperspace. Maybe you will find answers, but probably not. There is a drive for understanding that is innate to human beings, which in my opinion is what motivates a lot of what is on this forum. "The need for more information, the 'truth,'" and so on.
My prediction is that there is an objective reality, but it is a reality that can be perceived radically different by different beings. There is a place for beings to exist, but this may be the far-point of the conjecture or final theory. "We have a place." For you cannot predict how an alien, 3 dimensional or otherwise, will interpret what you interpret as reality.
I theorize that the multiverse exists along with a huge consciousness. How these things interact depends on your own theories and explorations. Are they the same thing exactly? Honestly I doubt it, but you will undoubtedly get those acid-heads who will tell you that we are the universe observing itself. I take that to be a very materialist view; I tend to think there is something more behind consciousness being unique and existing outside material objects.
But as always, theorizing and answering only brings more questions. Is our shared consciousness the only one? Even if the multiverse, if it is real, exists, are there even other multiverses outside of the realm of this one, just as the same theory suggests there are universes outside of our own that we don't necessarily have direct contact with yet?
And the most important question, does it even matter?