Can AI utilize the mods?

Simply put, yes. Unless if a mod author clearly states that it only affects the player, or if it affects something the AI can't use anyways (such as chat) then there is no reason why the AI wouldn't

Your question is actually two-fold. Will the AI make use of modded capabilities such as increased range? Yes, it will. The AI has access to exactly the same units you have access to, so it will be use those modded capabilities.

Will the AI build units, which are normally good, but made completely useless with a mod? That's something no one knows, because unless you are a modder yourself, how are you going to test it? A mod like this would never be released.

The AI can operate on two different directives:

1) Evaluate unit strength and choose units based on that. In this case, the AI wouldn't build a 1 strength swordsman. This is an advanced and thus expensive method of creating an AI.

2) Have fixed unit choices after a certain technology is reached. I.e. after researching iron owrking, build swordsman. In this case, the AI would build 1-strength swordsmen, even though they are useless. This is MUCH easier and cheaper to program, so many AIs would use this method and require extensive modification for mods.

Considering the default AI makes use of range 2 archers, which have less strength than melee units, throughout the game and the AI also uses gatling guns, I see no reason why they should stop making gatling guns later in the game even with reduced strength, no matter whether it's a Method 1 or 2 AI.

However, if you go for modding, I'd recommend you choose the Vox Populi mod, instead of a poorly balanced range increase, which hasn't been updated in four years. The folks from the VP-team have spent years honing, updating and balancing Civ 5.