You mean physically travelling to spiritual dimensions/planes? No, because they are not physical planes.

As to immortality also, no. First of all, 'immortal' means never dying, and even this planet will not last forever. That said, now that DNA has been discovered, it is apparent that manipulating the genetic code to end 'natural' death has been reduced to an engineering problem. It will happen, if we can maintain our technological vector long enough. Of course the substance of the human organism has it's needs and limits, so you will never be able to rule out accidental death - but that doesn't rule out living thousands of years or even tens of thousands of years, should we put our collective minds and energies to it.