OK, if you mean something like this the answer is yes, you can invoke your new code by that moment at any time during the page persistence within the browser, under the following conditions:
2) Even if your function declaration is inserted into a
block within an existing
element, the browser won't know the new function exists, as the declaration code has never been executed. So, you must
your declaration code returned by the Ajax callback, in order to effectively declare your new function and have it available during the whole page lifetime.
Even if quite dummy, this code explains the idea:
I didn't use Ajax, but the concept is the same (even if the example I chose sure isn't much smart :-)
Generally speaking, I do not question your solution design, i.e. whether it is more or less appropriate to externalize + generalize the function in a separate .js file and the like, but please take note that such a solution could raise further problems, especially if your Ajax invocations should repeat, i.e. if the context of the same function should change or in case the declared function persistence should be concerned, so maybe you should seriously consider to change your design to one of the suggested examples in this thread.
Finally, if I misunderstood your question, and you're talking about contextual invocation of the function when your Ajax callback returns, then my feeling is to suggest the Prototype approach described by krosenvold, as it is cross-browser, tested and fully functional, and this can give you a better roadmap for future implementations.