Can I safely run a LED light bulb from a UPS?
The LED lamp probably has a switching power supply with a capacitor and bridge rectifier. This would account for a brief arc and pop when screwed in since the capacitor could draw many amperes if it makes contact near the peak of the AC line. 

Since UPS units are designed to work with massive switching power supplies on PCs it seems unlikely that it would have damaged the UPS in any way.