Yes but it's something of a hack.
First, create a graphic in the package of your choice (Inkscape is a favourite of mine) for your watermark. This would be the word 'draft' for example. Make the page size of the graphic the same size and shape as the pages you're writing on in Libre Office and save it as a png. You can make it any shade or colour you like.
You can apply a background to any page by selecting
Format>Page>Background and selecting graphic instead of colour. Set the background to take up the whole page area then browse to your png file.
You can create page styles that include any number of watermarks selecting the
styles and formatting menu (F11) and going to page styles. Create a new page style and add your background using the process from the paragraph above. Save your new page style and you can apply it to any page you like. There's a screencast of this process on YouTube.