The idea that we could push a web app, and not test in the real world can send said app reeling. I heard a speaker make the connection between app store ratings and performance. We sadly don't have the same ratings system using web apps, outside of word of mouth.
As such, among the tests you must conduct prior to going live should be to replicate real world conditions as closely as possible. There are several ways to attempt and achieve such conditions, although none will ever recreate the messy and unpredictable conditions of the actual device in the streets.
From the throttling available in dev tools (Chrome + FireFox), to the Network Link Conditioner app on the Mac platform and the many other tools are our disposal, Patrick Meeman covers the pros and cons in using these tools in the essential requirements to test with realistic networking conditions. You can read it here.