Yes, I would think so.
There will be a lot of day trippers going to the city on matchday, there will also be a lot of fans without tickets going to that city for a few days to be 'in the matchday atmosphere'. Also like your group, 10 people go to the city but only 2 have match tickets.
Undoubtedly there will be some fans who stay in their base city on matchday, but I think the best plan is to head to the host city on matchday morning.
Depends on some other factors as well I guess, like how far away you are between cities, and cost etc.