It's fairly close, but of course there are differences. The King James translators were basing their Bible off of previous English translations and guided by the Textus Receptus rather than this manuscript or critical editions (which didn't exist yet). There were some politics involved that biased translations here and there, but the theological implications aren't that significant. And there are some mistakes in translation that slipped through.

The most significant difference between this text and the King James is probably the https://en.wikipedia.org/wiki/Comma_Johanneum , which is likely a forged addition to later Greek editions of the New Testament providing explicit textural support for the doctrine of the Trinity.

The King James translation is rather dated, though. Some modern translations are much, much better in the sense that they come from a reconstructed text using the earliest manuscripts and they use our modern knowledge of Koine Greek.