In the past, BBC America has aired multiple one-hour UK dramas (meaning 45-46 minutes without commercials) uncut in a 60-minute timeslot (Whitechapel, Law & Order: UK, etc.), so there is no reason to assume Broadchurch will be cut for time, at least for the first 7 episodes.
What happens with episode 8, which runs 50.5 minutes, depends on the ratings for the first 7 episodes. Last fall, The Hour S2, which ran 60 minutes, was initially given a 75-minute timeslot. However, the ratings were very low, so low that the final episodes were reduced to 45 minutes in a 60-minute timeslot to allow a repeat of Law & Order: UK, which got higher ratings, to air from 10-11pm.
If enough people watch Broadchurch, making the show profitable for BBC America, then the final episode could very well air unedited in a 60-minute timeslot with limited commercials. If the ratings are just OK, then BBC America might trim 4-5 minutes from the final episode.
On the subject of editing for time, I noticed something interesting with another BBC America show, Ripper Street. BBC America, which co-produces the show, aired 55-minute episodes in a 75-minute timeslot, while BBC One aired 59-minute episodes (I "found" the first few episodes online for comparison, and they all ran around 59 minutes). However, I just bought the S1 Blu-ray, and all episodes run 62-63 minutes, so it looks like even BBC One made edits before broadcast.