Pistachio cake

Has anyone tried this with gluten free flour?

HI Astrid! Echoing what's already been said here—you could make your own version, but you would need to add sugar (since the pistachio paste you'd buy is sweetened).

I would recommend a recipe specifically for paste rather than marzipan. They are similar, but marzipan has a higher ratio of sugar to nuts (whether almond, pistachio, or otherwise), so it's best not to interchange them. Here's a recipe for pistachio paste from the great Pierre Hermé: http://www.cuisinedaubery.com/recipe/pistachio-paste-pierre-herme/

It's like a pistachio version of marzipan...sugar nut paste.
Short answer, yes.
A recipe here:
https://www.thespruceeats.com/pistachio-marzipan-521099