How to know if a motorcycle battery and power generator is enough to keep an device turned on without discharging the battery?
In the comments you say that arduino and associated hardware will not be directly connected to the battery. That it will be on a switched/key circuit. If that's the case, it will not be an issue while off. This can still be an issue when the key is on but the bike has not been started. You want to minimize the current draw at that time.

While the bike is in, you need to know how much current or power/wattage your system is taking, and compare it to the available power on your motorcycle. Each one is different. Some boats (not like watercraft, but the same applies) have so many features and options that they can provide 10s of watts of extra power without issue. Smaller bikes with smaller generators/magnetos cannot spare as much. If you draw too much, you can fry your regulator or stator. Some bikes can have extra windings added to the stator or gave spare sections that you can add additional power output from.

Other options include replacing power hungry incandescent or halogen bulbs with power efficient leds, freeing up power for your add on project. 

That said, if your only adding a few watts, 5 maybe 10, your probably be okay just adding it on. Honestly I suggest hitting a forum specific for your motorcycle or a general motorcycle modders site for info.