The application starts up faster, and maybe the library file, if it's located on the SSD, but working with the photos saved on the HDD will be "crippled" by the HDD's speed.
The one thing people seem to forget is that an SSD isn't going to magically make a secondary HDD (internal or external) faster. It may access something faster and it will make everything that is on the SSD faster, but as it was said above the HDD is going to be crippled by the HDD's speed.