It would be possible to write a plugin for that, but that needs a developer experienced in C++ and interested cycloid math. I can add a feature request to github issues, but can't say if and when somebody will take this challenge.
The online calculator you have linked, already has the possibility to export DXF. I haven't tested this, are there any issues with that DXF?
Another option is to use the CSV output of that calculator or any other source which can calculate X/Y points on the cycloid. With the ASCII import plugin it should be possible to import the cycloid from a simple text file containing X/Y coordinates. Not the best solution, but it may work.
The file format for ASCII import is very simple (No.;X;Y):