Does changing the brand/type of guitar strings have any bearing on the sound of the guitar?

Yeah, it could definately change the sound, depending on whatgage they are or what they are lined with, like you said bronze. I copied this from a guitar site I like....maybe it can help Electric Strings: Nickel Plated - This string consists of nickel plated steel wraps around a steel core. The steel gives you better magnetic pull thus more volume electronically, and the nickel helps keep the steel from corroding. This is the most common type of electric string. Pure Nickel - This string consists of nickel wraps around a steel core. Due to the pure nickel content of the wrap this string is mellower in tone and has less output electronically. It gives that "vintage sound". Stainless Steel - The brightest material for electric strings, and has good volume electronically. The stainless steel is not as smooth to the touch as the nickel types of strings. Stainless steel is a very hard material and combined with its rougher texture, in my opinion, causes quicker fret wear

Phos bronze do sound warmer with more sustain than say nickel wrapped steel, which may sound tinnier.

Definetly yes and strings have a limited life before they start to sound plunky

i used to go all out for the perfect sound on my guitar but have to admit that even when the strings were old someone would come along and play it ten times better than me.

it will make a difference