I am attempting to do the same as @shub but when I do the above process "Bring in a shapefile of your contours and make sure they have an elevation attribute with them. Go to Raster > Conversion > Rasterize and select your shapefile, the elevation attribute, and then your existing Tiff file you want to put the contours on. Press run and you will get a tiff with the contours on top of the layer. Controlling line width when merging vector files into raster? is very helpful to accomplish this.
It runs but only recreates the geotiff orthomosaic but doesn't have the contours "burned" on to the geotiff.
My use case is golf course geotiff and contours/shp file generated from pix4d/drone imagery. I would like to be able to upload the geotiff to a web viewer and have the contours and preferably the labels/elevation displayed/stamped onto the image.