Yes you can can choose a layer on the page under “carte” button. “Partager” generates a permalink. Here is a link with full layers active : https://www.geoportail.vd.ch/map.htm?share=f413611c-6471-44fc-a4b4-4b58d6c7d3e3
There are already some links for VD on the Google Sheet shared by vince: https://docs.google.com/spreadsheets/d/1J5DQ_gV59CBm0gJQMbhFa8r-8umobqheZIQH6HmDOXk/edit#gid=1162213270