score:4
LDS commentary on this question is sparse, but based on the below information I infer that the answer is no.
βThe Holy Ghost as a personage of Spirit can no more be omnipresent in person than can the Father or the Son, but by his intelligence, his knowledge, his power and influence, over and through the laws of nature, he is and can be omnipresent throughout all the works of God (Joseph F. Smith, Gospel Doctrine, 61)
In other words, presence is related to knowledge, power, and influence over and through the laws of nature. These are areas where other spirits are deficient.
Each spirit child of Heavenly Father differs in intelligence. Jesus Christ is more intelligent than all of Heavenly Fatherβs spirit children, and His wisdom excels them all. The Pearl of Great Price: Teacher Manual, (2000), 44β46
Because other spirits don't have the perfect intelligence, knowledge, power, and influence of the Holy Ghost, they probably can't have omnipresence either.