I have an outside spigot in my garage that leaks when turned off. I had a hose connected on a hose cart and the hose would fill with water (when off) and eventually broke the hose cart apart (from the built up pressure I'm assuming). If I put on a hose cap or a hose with a nozzle on the end, could backed up water cause pressure and a burst somewhere? Or would this be sufficient in holding the leak?

You're thinking the wrong way. You don't "hold the leak" you fix it.
Shut the water off at the house shut off and unscrew the bonnet packing nut located under the handle. Back the stem and washer assembly out counter clockwise. Now run your fingernail around the seat. If you feel nicks or rough spots replace the spigot. If the seat's OK them replace the old washer. Reassemble and test. Better now? Good luck, Tom