As discussed under Jacob 1:14, Joseph Smith occasionally edited out redundant occurrences of the subject pronoun they. Such redundancy is frequently found in the original text when there is some delay between the initial occurrence of the subject and its associated predicate. For further discussion, see under subject repetition in volume 3. The critical edition will restore such examples of redundancy since they are clearly intended in the original text.
Note, by the way, that the generic plural pronoun they is used here rather than the singular he. Elsewhere the original text has examples of both they and he as the generic pronoun for whoso(ever); for discussion, see under 1 Nephi 17:48. Here in Mosiah 18:17, the original they works better than the singular he because of the potential confusion that would result if he were the subject of the clause (“he was added to his church”).
Summary: Restore in Mosiah 18:17 the original reading with its redundant use of the subject pronoun they: “whosoever was baptized by the power and authority of God they was added to his church”.