Yes, this can be done with a script, but a script is quite limited in the kind of links it can create, so it's better to do it with a stand-alone application (the latter is also more robust and can process large files without the fear of getting stuck).
I've developed both versions of this tool. You can find them both on my site, here: Custom-made Adobe Scripts: Acrobat -- Create Custom Links from Text
I had a look at the instructions of the standalone app, too bad it can only create links to fixed targets such as linking the Word "Service" to a service address. But this can definitely be very useful in specific situations, I made sure to bookmark the site!
In this case, the script would need to do the following:
1. Search for the text snippet "see chapter"
2. Fetch the chapter number that follows
3. Search for the headline with the same chapter number (identifiable as headline by its formatting)
4. Optionally create a named destination at the target headline
5. Link the text snipped to the named destination
You wrote that you already have named destinations for all the headings. If that's the case then you can use my tool to link to them. For example, you can tell it to link all the instances of "see chapter 4.6.1" to a NamedDest called "Chapter4.6.1".
It won't search the file and create the named destinations for you, if that's what you're after, though.