It is possible that the feed from your panel goes to more than just the furnace (e.g. heating control, water pumps, etc) but that is not going to be easy to find out under your current conditions.
If it looks as if only one breaker feeds the heating system, it might be best to disconnect that from the panel (having switched off the main supply first!) and then use your extension lead to power the disconnected wires feeding the heating system.
Keep the earth/ground wire in the panel, and just add your generator earth to the panel earth so you don't have some of the home on supply earth and the heating on you generator that might be "floating" as not having its own earth rod, etc.