It's probably going to be a military RPG. Non-combat roleplay will still be at least semi-military in nature. If you can imagin roleplaying a knight templar - or even a fantasy paladin or Navy SEAL, for that matter - you can imagine what playing a Space Marine might be like. Deathwatch is more unorthodox in its methodology than the chapters of origin, from which members are chosen. They're already veterans and can be trusted to schedule their own way of accomplishing tasks, and even though they'll still want to be grim hardcore warriors they have to cooperate with brothers who do things differently. Sometimes very differently. The kill-team will most likely also work close to an inquisitor, who can go about doing his job however he damn well pleases, and will expect his men to keep his pace.
The band of brothers theme will be strong. As a kill-team, working behind enemy lines, going into hot zones and assaulting strongpoints without backup will be common fare. They are an elite of elites, and will have more freedom and carry a higher degree of responsibility thanks to that. As I understand it, ex-Deathwatch members return different from when they left. They've seen, done and know things above and beyond even what the other Space Marines have experience with. The game will probably reflect that.
Space Marines have no use for spare time. Thus the 15 mins, when cloistered in their fortress-monastery. I doubt Deathwatch members have more time for leisure. And why would they want to? Who said being a soldier have to be about sitting around farting, occasionally firing your gun? Military service on their level encompasses more. Recon and other investigation, escort duties, building and guarding strongpoints and holy places, planning and tactics, the logistics behind setting up and keeping hidden bases, shipboard existence while travelling to and from a mission, certainly xeno-biology to pinpoint weaknesses, perhaps even diplomacy and politics in some cases.
Still, the question is if you're even interested in roleplaying a relatively single-minded, hardcore dogmatic/religious, merely near-human ultrawarrior? If not, Rogue Trader and/or Dark Heresy might be a better choice.