To some degree, possibly, but you can minimize the risk.
The substrate is the bed for the majority of bacteria in the aquarium. There are many more species of bacteria than just the nitrifying ones we most often think about. But the colony of the nitrifiers which are primarily responsible for the ammonia/nitrite/nitrate cycling usually (though not always) occur in the filter so keeping this running should avoid issues.
Bacteria also colonize every surface covered by water in the aquarium, including plants (fake or real), wood, rock, decor. Not letting any of these dry out and not cleaning them but keeping them wet in the existing tank water (in buckets or the temporary aquarium housing the fish) and then transferring them into the newly set-up tank without any rinsing or cleaning will transfer the bacteria over. Same for the filter.
I realize you do not have live plants, but just for the record I will mention that having live plants, especially floating plants which are fast growers, will make it impossible for there to be any cycling issues because of their capacity to take up ammonia.