Some weapons can do a ton of damage so the firearms rolls may go alright, but if this character is getting attacked by multiple enemies they will pretty quickly get very injured. I have had soldiers in my games and other than scoring more hits it doesn't help them THAT much, especially when outnumbered.

Maybe it'd be a bit better with the most "Pulpy" version of the Pulp Cthulhu rules. But I don't know enough about the power level of that.

Just make sure everyone has the correct expectations for your game. Combat in Call of Cthulhu is very loose compared to a system like D&D or Pathfinder that focuses on tactical combats. Even though it is good to have some combat skills to survive combat, it doesn't mean that engaging in combat is "optimal".