BBC America airs plenty of shows in extended slots to air them in full, and while they do censor some content on some shows, I think assuming that every show is edited in some way is going too far. New episodes of Top Gear air in a 90-minute slot, so the entire original episode will be shown to US audiences. Every episode of Doctor Who airs uncut during its premiere (the Christmas specials are often cut down to 45 minutes for repeats). Hour-long BBC dramas like Luther, Being Human and Ripper Street are given 75-minute timeslots (however, in some cases, these shows are trimmed from 58-59 minutes to 55 minutes, though from previous viewings/comparisons, the cut footage is mainly establishing shots of streets and such, which contain no dialogue).
Back to the specific question raised above, Broadchurch aired on ITV in the UK, which is a commercial network (as opposed to the BBC channels, which are commercial-free), so it was a 60-minute show with commercials. So at least in terms of time, BBC America should be airing each episode of Broadchurch in full from 10-11pm, as they have done for other "60 minute with commercials" shows in the past (like Whitechapel). Based on the IMDB Parent's Guide for Broadchurch, brief rear nudity in Episode 5 might be blurred (though brief nudity has appeared uncensored in original TV-MA dramas like Orphan Black and Copper, so it depends if BBC America wants to give Broadchurch a TV-14 or a TV-MA rating) and one use of the f-word in Episode 5 will be censored (BBC America routinely allows cursing up to and including the s-word).
I'll definitely be tuning in to BBC America for Broadchurch, since the minor censoring that will most likely occur won't disrupt the flow of the story/action (I would never watch something like The Inbetweeners on BBC America, for example, because so much language would be censored that it renders the show unwatchable).