Problem with Mercenaries large scale combat system is ok it tells you what happens when you finally meet a unit but it doesn't (I don't think from memory) tell you how to work out tracking and avoidance, surprise, how to calculate unit encounter size, etc. And then there are loads of things that take place in the standard war game such as plane combat, helicopters, recon units, artillery, communications, and intelligence/counter intelligence etc. So to try to create an actual war using purely Mercenary system would be rather difficult because Traveller is just not suited to large scale combat and apart from that few pages it isn't covered anywhere else in Traveller at all.
So you have your work cut out trying to administer a war game using the rules as is, you need to come up with an abstract system or your own, never mind keeping the players interested whilst you are administering all that stuff.
Now in order to role play, once you get all that sorted, it all depends what the characters are responsible for - are they grunts, commanders, a special unit? As Traveller needs to keep the character together and have them liaising together for any kind of interesting game I would say the best thing to do might be to make them an SAS type unit with the war going on around them. Otherwise you will have to have a heck of a lot of imagination to visualise a detailed war with the stuff provided.
So make them a SAS team, give them specific missions such as spying, recon, destruction, assassination etc and just keep the background war stuff to regular reports from HQ. They could always occasionally come up against overwhelming odds in which case they could call up assistance but I really don't see how you could involve the characters in a massive war whilst keeping them interested. The SAS type route would at least give them responsibility for equipment, training and recruitment (you could use some NPCs for redshirts that are likely to die) and they could always be other items such as conflict with their superior or other friendly forces that they have to work with or rely on (like cavalry or helicopters leaving them stranded).
Fact is if you think of any interesting war films its always concentrating on small elements within the war never just the war itself - Saving Private Ryan, The Longest Day, Full Metal Jacket being good examples of how to do role playing whilst having the big picture around the characters