Having enough power to affect natural phenomena, like the weather, seems to require the sealing power but doesn't require one to be Christ. Every prophet in the scriptures who we're told affected the weather (usually through withholding or sending rain, such as Elijah
) was given the sealing power and, more importantly, had direct communication with God, other than the Holy Ghost. In Nephi's case, we're also blessed with an account of how
he sealed up the heavens and unsealed them: through reasoning with the Lord
. Because it would require reasoning with the Lord Omnipotent of heaven and earth, one would have to have a truly righteous reason to calm the storm- in Jesus' case, calming the storm was both a physical manifestation of His power for the disciples' sake, and symbolic of His power to calm spiritual storms.
The question could be reworded as "does a person have enough power
in their priesthood" to perform such-and-such a miracle (in this case, calming the storm). Power and authority are two different things; a man could technically have priesthood authority but no power to back it up. Priesthood power is inseperably connected to a person's level of faith in the Lord. With sufficient faith and the proper authority and the right reasons, you could
command the storm to be still, and it would be done.
However, Melchizedek "quenched the violence of fire" (JST Gen. 14:26
) through faith, so it seems that faith is the operating principle in affecting nature and its forces. Indeed it must be, if it is the power by which God Himself operates! So I think a prayer with enough faith, from someone without priesthood authority, could also be honored, although it would probably be honored as a protection for the individual from the violence of the storm, not stopping the storm itself.