I think that's probably the best bet for Traveller. Borrow the grand scope, theatrical flair and narrative style of Mass Effect but retool it to fit the system.
The problem with highly structured campaigns remains, the tendency for players to want to buck off in their own directions and bust up any attempt at a "path" oriented approach, which is normally handled in Traveller by designing a sandbox for just that kind of player to play in. But if you're entertaining enough and your players are happy to cooperate in the right spirit it can work.
Mass Effect tries to create the illusion of a sandbox, multiple optional side missions and the ability to roam about at will, but ultimately there's a straight line through the major plot points the players must encounter. ME3 is rather interesting for the conceit that you're building up a big alliance to take on the Reapers so wandering around and discovering new resources gets a thumbs up. But that's a purely gameplay device. In reality I suspect most players would keep their eyes on big picture stuff and not want to go haring off to scan random sectors in hopes of finding some indefinite reward. Pure exploration made a bit more sense in ME1 because you are exploring regions somewhat new to humanity. In ME3 and ME2 it really was never a great fit but players like that illusion of freedom, myself included, so they had to leave it tacked on.
For me the most important feature, the most important aspect, of the ME series is memorable NPCs. You're going to want to build not only allies and enemies but whole chunks of the universe that revolve around them. Draw the players into the world through the interaction with NPCs and ones drawn more colorfully than the usual Traveller Patron contact. If you have creative players get them talking about their character's pasts during chargen and make sure their NPC contacts might well end up driving the story. If you already have crucial NPCs that might fight the role suggest them to the player (and keep in mind this potential while designing the NPCs).
Fit as much story as you can into the context of something coming out of an NPC's mouth. Play down computer libraries or generic rumors. If an investigation roll turns something up put have an NPC in mind that this might lead to rather than just a handful of facts and leads. Most of these NPCs will probably want something in return for the information. Some will become recurring characters, some might even become crew, while others will remain more in the background (Shadow Broker, Illusive Man, etc.).
Dramatic scenes will be harder to plan as you can't really script a player's behavior, and dialogue, the way cutscenes in Mass Effect do. All you can do is figure out where something very dramatic is going to take place and describe it as vividly as possible: the surface of an asteroid hurtling towards certain doom, a concealed base in a dense jungle or under a volcano, etc. Think ridiculously big and don't let Traveller's inherently sober nature hold you back.
Pull all kinds of little tricks to keep players on their toes like flashbacks or dreams but with no warning - especially with psionic characters. Just turn to a player and start in on it. By the time it's over they'll know what's going on. Have them stumble across situations that are already in progress and make them pick sides based on limited information and under pressure. Mistakes, even forced ones, are opportunities for good roleplaying. Characters in Mass Effect often carry around regrets, misconceptions, and second guess themselves. That creates opportunity for redemption and surprise twists if handled correctly.
The beauty of Mass Effect is that it gets a player, even someone who might not be a natural roleplayer, into the mindset of the character and gives them strong local settings and vivid NPCs to form associations with. Traveller games tend to be less over-the-top and more grounded. That's not at all a bad thing, that's Firefly and I love me some Firefly, but it's not where Traveller necessarily shines. Traveller's combat alone tends to be much more deadly than Mass Effects and "save/resume" isn't an option. Doesn't mean you can't do it though.