I think it depends on the master's. I started the app process (specifically, prepping for the April MCAT) in my last semester of my MBA program. It was difficult to both study for the MCAT and keep up with the classes because they required different mindsets, but it was doable.
On the other hand, I know a guy who got a master's in biology (I don't remember the area of emphasis); he applied while he was doing his thesis. He had excellent grades, MCAT and LORs, but didn't get any interviews. This, he said, was because he was so distracted with his thesis that he didn't get his apps in until the deadlines, which probably put him at a disadvantage.
Finally, I met a guy at an interview who said he'd done 10 interviews in six weeks on the East Coast (he was from Texas), and had to keep flying back and forth in order to keep his research on-track while interviewing. If he was being truthful, kudos to him...it would have really stressed me out if it was me.
Bottom line - look at what your workload will be at the time you're applying, and plan accordingly. The MCAT, AMCAS, secondaries, and interviews are all time-intensive and distracting and should be treated as such, but if you're good at time management anything is possible. Just my $0.02.
