Do you need a spark plug resistor cap to run a motorcycle?

I'm tryna get my Honda 90 running and when I was pulling it apart the spark plug cap came off and broke. Does the spark plug need the cap to function or can I leave it?

If you could leave it off it would not be there in the first place.
OF COURSE YOU NEED IT!

You don't need the insulator boot over the plug wire for your engine to run. If the conductive wire can reach the top of the spark plug, the circuit will be complete.
Ford Model A's & T's spark plug wires were just screwed to the plug top with no insulation boot. The boot, along with the ribs on the porcelain insulating the spark plugs electrode, are meant to deter the spark from traveling along the outer surface of the plug, thus shorting it out, and not jumping the gap in the combustion chamber as it should.
Electricity will travel the easiest path to ground.
If you can get the conductive wire to reach the plugs top, it SHOULD work, at least for now.

Like, the resistor is buried in the body of the plug, dude. I've seen a rat-bike run with bare household solid copper wire on the plug with no spark plug boot or aluminum cap at all. So do that and place your tongue on the bare wire on top of the plug as it tries to start. You'll sense whether it's getting any juice.

Connect the wire direct and it will work. The resistor is there to prevent radio interference that upsets people watching TV near where you ride

If your bike has CDI ignition, you need the cap.

Get a new cap, they're like $5

Resistor cap for plain plug was for radio interference mostly. I use the Marine Sparkie caps for weather protection, rain may short a bare wire on plug- for some replacements. Depends on motorcycle and sparkplug location- on some DOHC engines the long 'resistor' cap is needed just to reach the plug near buried in cam towers, hard to get a cable end and bare wire to attach to plug. Flathead lawnmowers on the other hand may have plug sticking up, easy to get to and simple loop in wire or a fork end to go under removable cap.

No, you don't need it. However if the gas tank is weeping gasoline and your spark plug wire is not on tight, it lights up and burns. The bike. So it is a safety thing.

Buy a new cap, Check the compression, If that's good, clean the fuel tank and carb, adjust the valves and clean or replace the air cleaner, adjust the ignition timing.