Technically I think yes, it may have a finite extent. If inflation theory is correct though, it will continue to inflate at extreme rates (if unevenly) for infinite time and so depending on how you think about infinity will have infinite extent in spacetime.

On the other hand if Roger Penrose is correct about Conformal Cyclic Cosmology, and cosmic inflation is false, then ultimately the universe will reach a state where scale ceases to matter and it will become mathematically indistinguishable from a hot dense big bang again.

https://en.wikipedia.org/wiki/Conformal_cyclic_cosmology