A fire extinguisher is always a must have in any shop, vehicle, or whatever.
Chances are if your paint booth were to have a fire the extinguisher will do little to no good.
When air in the booth reaches the LEL of the solvents being sprayed and
IF there is an ignition source then you have a BOOM or flash fire, then maybe fire.
Most likely You probably won't be in any condition to use the extinguisher at that point.
The LEL for urethane clear is around 1.0 and the UEL is around 13.1.
That means if the atmosphere in your "booth" is 1% urethane than it is possible to have ignition.
If the atmosphere is above 13.1 urethane then the mixture is to rich to ignite.
Anywhere in between will ignite.
This information is available in the MSDS sheet for any chemical you use.