"Flirt to convert" is heavily frowned upon. If you want lasting conversion that isn't going to evaporate as soon as the missionary gets transferred, you want it based on more than just the comeliness of the messenger.
I think male and female missionaries both fill important niches. I would compare it to my field--psychology and family therapy. The majority of professionals in my field are female. At the clinic where I work, lot of clients specifically request a female therapist (it tends to happen the most, in my experience) when the presenting issue is sexual abuse and the client is female). Some specifically request a male therapist (fewer are in this category--I see it most when the client is a male child). The majority of our self-referred clients are female. The majority of our court-referred clients are male. The majority of our parent-referred clients are male. So you can see there definitely are gender issues at play when it comes to therapy. As a male therapist, I can often see that my gender matters to some clients. But when we first start a therapeutic relationship, gender seems to matter more to people than it does after we get past first impressions.
Like Eran said though, when you get beyond the initial interest factor, gender plays less of a role than other factors (like your competence, your personality, etc.). I would think the same is true for missionaries. Some people will probably let missionaries in their door just because of their gender (or turn them away based on gender), but after that initial contact, it probably doesn't matter as much.
As far as people in suits and ties with literature in hand seeming creepy, I can only say that sounds like a sign of the times. I have noticed that an increasing number of young people find a lot of things creepy that used to have positive connotations, such as caroling in a group, chatting around the dinnertable with their family, going camping with their family, giving volunteer service at a homeless shelter, praying out loud with others, helping out with a fundraiser, performing on stage, etc. A lot of these have to do with our growing social incompetence, which has complex roots but includes causes like less face-to-face entertainment, less face-to-face communication, lower expectations from parents for their kids to go out and do things that are character building but uncomfortable, less emphasis on character in general and more emphasis on fun, and so on.
The idea of college-age young people going out of their comfort zone and approaching others about something they are passionate and enthusiastic about, while wearing a uniform attire, and possibly facing repeated rejection (at an age when supposedly they should be focused on getting drunk and laid at some party school) seems so alien to a lot of young people that they can feel immediately distrustful of someone else who is willing to do such a thing day after day. A lot of people can't fathom how someone would willingly serve a mission under those conditions, so they immediately question their motives and their sincerity. Negative attributions are made to try to explain the discrepancy between what you could rationally imagine yourself doing, and what you see these two guys in suits doing. So you get negative assumptions like that the two guys in suits with literature in hand must have a shallow understanding of what they are promoting, must have been brainwashed, must have someone back home bribing them to do it, etc.
All I can say to that is, you'd be amazed at what you can learn when you sit down and talk to these young men and women who are serving 24 or 18 months (respectively) of their prime years, usually at their own expense. Even if you aren't interested in their message and avoid the topic of religion entirely, it is pretty inspiring and impressive to just ask them what makes them tick and what motivates them to come out and do what they are doing.
You'll find a vast range of experiences. Some are recent converts, while some grew up with Mormonism from the start. Some have struggled with their faith and have only recently come to a point of personal conviction. Some have saved up since the time they were 8 years old for this opportunity. Some have put a promising college sports career on hold to come out and serve. Many have a boyfriend or girlfriend back home that they hope will still be there when they get back, but they know full well that there's no guarantee. Some are there just because it was always expected of them, and fit the stereotype of the passive follower with the shallow personal identity. Some are very passionate. Some are very atriculate. Some are simple farmer types. Some are on track to becoming a lawyer or doctor. You'll find all types.