Yes, sort of.
There is no support for adding the sliding doors script. But you could use it to control the contents of the sliding doors menu, and add the sliding doors script either into your theme, or into a custom plugin.
I did this for one of our [iurl=https://geek.hellyer.kiwi/services/premium-support/]Premium Support members[/iurl] once. They seemed happy with it, but it’s not something I’m intending to roll into the core of the plugin as it tends to result in a lot of support requests due to the CSS in the sidebars being far more likely to glitch than a simple dropdown (because sidebars tend to include their own unordered list styling).