I'm wondering if the choice of the strings on this guitar could have a very significant impact on its sound and playability.
Yes, definitely. Well, I suppose it might depend on what you consider "significant". In terms of the sound, the change between string gauges can be subtle, but I notice it right away on my guitars - perhaps because I'm so familiar with how they sound. I might not notice as easily if someone else changed guages on their guitar.
But there's no question that string guage affects playability. That and the setup of the guitar (neck relief, neck angle, saddle height, nut slot depth, etc.) are pretty much the only things that can be changed that affect the playability. Neck geometry and bridge and body design are the only other factors I can think of, but they can't be changed without changing major parts of the guitar.
Lighter guage strings require less finger pressure to fret or bend, and tend to have a thinner, brighter sound. The ease of bending lighter strings has a downside in that it's easier to accidentally bend them which can worsen intonation.
Heavier strings require more force to fret and bend and can be harder to play, and they usually have a fatter sound that might be slightly less bright. They can actually be a bit easier to play in some ways in that you have better tactile feedback and better intonation.
Personally I find that I like heavier guages, even for playability, because it seems like heavier guages tend to have a smaller maximum displacement when vibrating, possibly because they have to be under higher tension. That means that I can have a lower setup with less neck relief without fret buzz. By having a flatter setup and using the minimal pressure necessary and optimum finger placement, I can play more cleanly with better intonation and I find the guitar feels better.
The point of the last paragraph is to say that one shouldn't assume that it's a simple equation of "thinner is easier to play and thicker sounds better". There are lots of different interactions with string guage, sound, and playability, and the setup of the guitar is affected by the guage and affects playability, so there are many variables at work.