Paradox titles produced on the EU clausewitz engine is notoriously unstable in multiplayer. MP has not been a priority for Paradox so there are generally massive sync errors in those games that scale in severity based on the speed you run.
Now, running the games via LAN will help the issue, but it will not entirely fix it. You may get lucky and have no problems, or you may be unlucky and find that due to your specific hardware configs the games are basically unplayable in multi, or you might be middle of the road somewhere and have the odd problem.
As for the Total War games, the last two have the kind of campaign you are looking for. Napoleon Total War and Shogun 2 Total War have multiplayer campaigns. However, the last I heard, they also have SOME issues with save games going out of sync or becoming corrupted.
Do some research would be my advice for TW. For Paradox, those games are all worth a buy strictly for single player and if you can get some MP mileage out of them (they are fecking brilliant in MP when they work) even better.