Yes, check the box for "Different first page" on the Layout tab of Page
Setup and anchor your watermark to the First Page Header only. If you've
already inserted the watermark, you'll need to:

1. View | Header and Footer.

2. Click Show Next if necessary to display the Header (as opposed to the
First Page Header).

3. Click on the watermark to select; Ctrl+X to Cut.

4. Show Previous to go to the First Page Header; Ctrl+V to paste.