Does a splitter still reduce signal if only 1 of its ports is used?
The splitter does not have a datasheet so it is impossible to know what topology is used inside that specific item. When used properly (with terminators)  the attenuation of a typical passive splitter is fixed. 

The insertion loss is associated with the device itself, and is a decrease in power delivered to the output due to the impedance network inside a typical passive splitter. 

Attenuation would depend on the connected load, however, you should be terminating unused ports with the proper termination resistance. When using the appropriate terminators the attenuation is fixed, nominally -6dB for a typical passive 4-port splitter. 

Unterminated, unbalanced, or shorted connections will cause reflections, and the effective attenuation depends on the interference of these reflections in the splitter.