Geany can be configured to execute any command, so it can run remotely if you can run a command (or script) to do so.
Debugging is not part of Geany itself, its provided by a number of plugins, see .https://github.com/geany/geany-plugins. All of the debugger plugins use gdb which I understand can do remote debugging, but you will need to investigate those plugins to see if they can run GDB in that mode.