In principle yes (if it is not against the app store guidelines). But if submitted as an app, it cannot use JIT compiling for security reasons. This will make the speed of JavaScript execution very non-competitive to WebKit.
Apps should be self-contained in their bundles, and may
not read or write data outside the designated container
area, nor may they download, install, or execute code,
including other apps.
So your can't ship a JS interpreter either, even without a JIT.
And section 2.5.6:
Apps that browse the web must use the appropriate WebKit
framework and WebKit Javascript.
So you just can't have a web browser not using the built-in WebKit, period.
As far as I can tell, you can install a web rendering engine that is not the built-in WebKit, as long as you only use it for HTML/JS that come with your app. At that point the JIT caveat applies.
You can ship a JS interpreter, it just can’t download code from the internet and run it (yes this makes shipping a browser in the App Store impossible).
But regardless, with your own device, you can run whatever code you want on it.