Today, the answer is “No!” But that was not always the case.
The current missionary handbook reads: “Do not flirt or associate inappropriately with anyone. Limit physical contact with someone of the opposite gender to a handshake.” But in 1887, missionaries had a lot more freedom. Edward Davis, who was a missionary in England at that time, is a case in point.
In Davis’s day, missionaries were often in their 20s and 30s, already married, and (because polygamy was still practiced) may have had two or more wives. Some of these men felt free to look for additional wives while on their missions. The letters of Martha Hughes Cannon to her husband, Angus Munn Cannon, give us a glimpse into what was on Davis’s mind.
Mattie roomed for a time with “Mrs. Hull,” (a pseudonym for the wealthy Anna Meyer) a fellow polygamous exile in England. Mattie and Anna met Davis at the Notting Hill Branch in London, where Anna had collected a “number of satellites around her in the form of English Saints & Utah Elders who bask in the warmth of her hospitality.” Apparently, she was generous with her money. But like so many of the plural wives in exile in England, she was not happy, and talked “of going home with Bro. Davis of Bear Lake for whom she had formed a strong friendship.”
Davis had enjoyed a solid reputation among the other missionaries. According to Mattie, he was thought to be “a very pious, zealous, straight walking missionary.” In fact, the young missionaries called him “too strait laced.”
Yet once he fell under the spell of Anna Meyer and realized she could help him out financially, that changed. Mattie wrote that Anna “cried to me & said he, Davis, had been wheedling money out of her—had got five pounds ($25) out of her one way or another, had borrowed [another] five pounds, and in coming from the station to my place that day had asked her for a third five pounds, which she said she did not promise to let him have. In addition to this she had furnished the means to emigrate one young girl upon his solicitation. And last but not least, that he was one of the worst huggers, kissers & slaubberers [sic] she had ever met, & that she was positive he was trying to get her away from [her husband].” The slang of the time for kissing was “lolly-popping” and Davis was apparently quite proficient!
Mattie’s husband, Angus, was the president of the Salt Lake Stake and very strait-laced himself. His responded, “I am gratified to know you realize I appreciate your kisses by letter while absent, rather than through Brother Davis. I read him correctly years ago, I regret to say. I am not surprised.” And in a later letter: “[Davis] was foolish to spend his time kissing while on a mission. It leads to no good.”
Things reached a crescendo when Anna realized she was not the only one Davis was so attentive to. Mattie reported to her husband that Anna had said: “‘I believe he [Davis] hugs & kisses every woman he can get hold of. I am certain he slaubbers [sic] over Sr. [Sister] Young worse than he did me.’ You see,” Mattie wrote, “the dear fellow sympathizes with women whom he thinks mismated. I suppose he thinks I have the right kind of a fellow, as he did not attempt any of his sweetness on me. I don’t know what sort of report he made to you, as I made no effort to court his favor—not even when I thought him most devout.”
Despite behaving as if the mission field was a hunting ground for a wife (or a fortune), Davis managed to pull himself together before he returned to Utah. He left with a good report of his efforts and by October 1887 was teaching school in Paris, Idaho. Anna went to stay with her relatives in Basel, Switzerland. Mattie Cannon was back in Utah by June 1888.
Missionaries in 2024 and in 1887—different standards for different times. And unlike those in 1887, today’s missionaries should not be found lolly-popping.

Re: today’s missionaries should not be found lolly-popping.
Aha! You say it’s OK unless they are “found”?
I had a companion who, a few weeks before the end of his mission, signed papers to marry a Colombian young woman so that he could fly her back to the U.S. with him and really get married, perhaps in the temple. However, the mission president found out about it and sent him home early. The elder’s father was very unhappy about it and accused the mission of trying to get out of paying for his return airfare. (I never witnessed any lolly-popping.)