Will companions/settlers still run out of ammo if I give them a matching gun?

If I give a gun that uses the same ammo type as the default gun carried by companions/settlers, will they still run out of ammo?

For instance, all settlers carry a standard pipe pistol using the .38 bullet. If I give them an upgraded pipe auto pistol or pipe rifle will they now need bullets?

Piper uses a standard 10mm pistol. I crafted a much stronger one to give to her hoping she would use it instead of her normal 10mm. unfortunately when i equiped it to her she pulled it out, then when we got into combat went back to her default 10mm :(

Yep, unfortunately you do need to give the companions ammo. Sometimes I've noticed when looting a body or a "dungeon" rewards chest (like they always had in Skyrim, except these are commonly the Army green steamer trunks) Cait will ask me for small rounds/ammo if she ran out on her AsSault Rifle. Surely enough she burns through ammo quite quickly. I'd suggest running her with melee (since she WAS a pit fighter and a damn good one at that) with decent armor with boosting stats like Strengthened or something. Best of luck!

For settlers things work slightly differently than with companions. As noted in previous answers, companions do use ammo for their equipped weapon, other than their default.

Settlers still require ammo to use a gun but it doesn't seem to get consumed when they fire. This means they only need to carry 1 ammo... equip someone with a minigun and 1 ammo, they can blast away all day!

There do seems to be some exceptions for this though. Mini nukes for the fatman do actually get consumed and I'd guess (although haven't tested) that this is also true for missiles.