It depends on what might be slowing your web application down :) I know "it depends" is so often the answer, but it's still true.
Anyway, I've asked around and it seems that Grails and invokedynamic won't go together just yet. The reloading agent needs updating and there may be problems with the cglib/asm libraries used by Hibernate.
Regardless, internally Grails is making more and more use of @CompileStatic (for the stuff that wasn't already written in Java), so unless your app is doing a lot of work itself, you're unlikely to see a big boost with invokedynamic.
It would be useful to have some official information on this, but it's not out there right now.