Running engine without ignition condenser/capacitor

tl;dr: Is the capacitor inside a 97 Corolla’s distributor important?

A few months ago my 97 Corolla wouldn’t start. After some investigating we found what looked to me like a bad capacitor (plastic gunk was oozing out). We removed it and the car started running fine.

Finding a replacement part has been tough. So my questions:

1) Is that capacitor thing the “condenser?” Am I searching for the right thing?

2) Is it important? Depending on what I read its purpose is either to make the radio sound better or to improve spark timing. The radio works fine, so if that’s all it’s for then I won’t bother with replacing it. But spark timing seems important…

Edit: Here is a pic of the capacitor.