I have a letter set up as a layout and it uses merged fields to populate the letter. However as the letter expands depending on the data an image of a signature sometimes overwrites the text.

Is there a way of inserting the image as a merged field?

No, you can't insert it as a merged field in a text block.

But you can put the container field into a separate part on the layout below the body.

A footer is an obvious first choice, but it has its limits on formatting and may not integrate into your letter as desired.

You could try a Sub-summary (Trailing) part. You'll need to add additional things such as a dummy field to sort by to make it work properly.

Stretch the text block to be as tall as it can ever be. Place the signature beneath it, select both and make them slide up, also reducing the size of the enclosing part.

Note that this will work in Preview/Print, not in Browse.