Disclaimer: I have not actually tested this. Nor have I actually investigated exactly how an nvarchar(MAX) value is stored as an included column in an index. What follows is a theoretical discussion based on general assumptions based on my general knowledge about how data is stored on disk.
An nvarchar(MAX) value can be stored in-row or out-of-row. If it is more than 8000 bytes in length it will always be stored out-of-row, and all that is stored in-row is a 16-byte pointer. If the value is smaller, it may be stored in-row, but there is a table option to force it to always be out of row.
If the value is stored out-of-row, the 16-byte pointer is all there is in the index. Thus updates to the value itself will not affect the index, so there will be no frragmentation.
If the value is stored in-row, this means that updates needs to write both to the data pages and the index page. And if the value changes in size, and increases in length, this can lead to that there is no space on the page, and therefore the page must be split, which can lead to fragmentation.
To sum up: what will happen in your case depends largely on the size of the data in the nvarchar(MAX) column.