My impression as an outsider who went to school in Utah for a couple of years is yes, on the whole courtships are whirlwind events (and the divorce rate is a lot higher than I expected). The prohibition against sex outside of marriage is strong, so people tend to hurry along so they can hit the hay in a moral context.
Of the dozen or so girls in my immediate circle freshman year, eight of them got married over the next summer, or even before school ended. One over Christmas break to a returned missionary she met at Thanksgiving. (To be fair, one of them was a Catholic couple.) And I think only two of them were still married to each other ten years later, temple marriages not withstanding. Apparently there's a sort of annulment procedure where you say "oops, didn't mean it"?
Anyway, yeah, not a lot of waiting around, in my somewhat outdated experience.