my temp guage failed will this prevent my radiators from flowing when the engine gets hot?

No, your coolant will still flow through the system. The thermostat that allows flow is purely mechanical and will still open when the coolant reaches temperature. Your gauge however may rely on the engine temperature sensor. You may want to get that sensor looked at ASAP due to the fact that it may control your cooling fans as well.

Temp gauge is simply a monitoring system of your radiators. Does not interrupt the function of cooling system as described above. You want this item fixed. Like humans, the 911 function at normal temps. Monitored those temps. The 911 will last for a long, long time with good temps and clean oil.