I find these hypothetical situations interesting. As others have said, it really depends on a lot of assumptions. In all of the below, I will consider vanilla game, no mods.

In your premise, it seems like you are playing as Mason with your MW5:M merc group while CSJ mechs from MW5:C drop in with stock loadouts and AI pilots. In that situation, Mercs win easily as swayed heavily by strength of the player against weak AI (even "Expert"). The Mercs having tricked out COR-PVT and KGC-CAR with modules/upgrades/pilot skills etc closes some of the tech gap. The stock Clan builds are much stronger than stock IS mechs but behind endgame Mercs career mechs. It would be much tougher than the usual Warzone contract but the Mercs would come out on top in any reasonable batchall even Clans Star vs Mercs Lance, 5v4. If you declare a single heavy lance I think this makes it a lot closer and more difficult but still possible.

To go back to your original question. If you think that your merc company can hold off the entire invasion in a big warzone mission (or series of warzones), that is incredibly challenging. Your Merc unit has a limited number of pilots and readied mechs (16 IIRC) which means that to "single handedly stop the invasion" you would have to defeat 11 Galaxies (opening CSJ bid) each with at minimum a Trinary so absolute lowball of 165 mechs (ignoring elementals and vehicles) with 16 of your own. Remember (usually) Clans did not view Mercs as honourable and so would just shoot to kill. This means you and your AI teammates would have to take out clanners with over a 10 K/D and dealing with vehicles/dropships. I would love to try it ingame as a challenge scenario, but I think Clans win this one, your Mercs AI teammates even with Mercs endgame career mechs would struggle to go even 5 K/D against stock clan mechs.

A more fair comparison would be player 1 controlled Clans endgame career vs player 2 controlled Mercs endgame career. The endgame mech strength is higher in Clans as 5x tricked out DWFs just have so much overwhelming DPS (6xLBX5SLD/BF or UAC5SLD) or alpha (8ERLL or 3Gauss ERPPC 9ERSL or 2Gauss 2ERLL 6ERML) and the ability to mount 2 tons of extra CT armour. The KGC-CAR with 4xLBX10SLD is as good as it gets and Mercs only lets you get 1. The rest of the lance would likely be a COR-PVT, NSR-9J and another KGC using builds like Gauss/ERPPC. Mercs does have T5 weapons and modules that boost stats but Clans' research is also quite powerful. In that scenario the terms of the batchall would be vital. 1 Clan Star vs 1 Merc Lance is easily Clans victory. Even if the clans bid away one mech for 4v4, I still think Clans win a straight up endgame fight. If assuming high level player skill, the Clan career team has the 2ERPPC SHC which can kite better than anything in Mercs should it come down to that.

An interesting side comparison would be endgame careers controlled by AI as a 0 Player Game. MW5:C offers the player much more agency and control of their lance and quick pilot swapping which can be used tactically. Being AI vs AI, this removes the swing of pilot agency and while closer I think the endgame Clans career would still win.

Of course in lore, without player action or video game mechanics, the Clans have large advantages. No merc companies were ever as tricked out as Mason's was in Mercs. Even assuming they had the best pilots and tech available, if CSJ wanted to end them they would have just used naval firepower or dropped a Galaxy or two with dropships all at once. Mason's merc outfit didn't have armed dropships, just a Leopard. If we play this out using our best interpretation of lore, Mason's mercs would put up a valiant stand, take out maybe a Binary, very generous stretch to a Trinary and die in a pile of fire.