Impacting networking affects the entire machine, especially in so far as a computer is increasingly just a dumb terminal to something else.
Look, If you make network requests potentially 20% slower then the browser performance will be impacted too, it's so obvious that I'm not sure how I can explain it simpler.
By how much? I am not sure, but you can't say it won't be slower at all unless we're talking about magic.
Pretending that it's trivial amounts of performance drop without evidence is the wrong approach. Show me how you can have similar performance with 20% increase in latency and I will change my stance here.
As it stands there are two things I know to be true:
Browsers rely on networking (as do many things, btw) and software is increasingly slow to provide similar value these days.