Is it possible to manually add elevation to trackpoints

It's not possible in BaseCamp, but you can do it by editing the gpx file in a text editor. If that method is too hardcore for you, there is a tool to convert a gpx file to a table you can cut and paste into your favourite spreadsheet program, edit the data in there and convert it back to a gpx file with this online tool: https://www.javawa.nl/track2table.html

The text is in Dutch; a translation button can be found on the left.

Have you tried using a Topo map when adding new points to your track?  I could be wrong, but  I think elevation data is only present with Topo maps.

Thanks for the replies. I decided to copy a nearby point then move it to the desired place.  If it had been more than a few points on a low slope surface, I would have just run it through GPS Visualizer.  

If you want to do it in BC and don't have a Topo map installed, an alternative is to install one of the free OSM maps with a built in digital elevation model such as Freizeitkarte. You can then use BC to Set Selected Track to Map Elevation to add the elevation data to your new track points (this will reset all the others too, like the GPS Visualizer method).