Not in the case of an instrument outside of the channel.
There is an important difference if we talk about effects inside the mixer channel, gain in the mixer, defines the level that enters in your effects chain, the mixer eq, comp etc. So gain is pre everything, the fader is post everything. And the gain in a device, well it depends on if it is an input gain or an output gain. But that's imho the main difference. So gain will have an effect on what a compressor does, because of the threshold. Imagine you have a threshold of -10 and a signal clips at -13, if you want to compress 1,5 db, you could set up the threshold to -13 and a ration of 1:2. Or you could add 6 db gain, and keep the ratio at -10.
That being said, I prefer to use gain to set an initial level for each device in the mix, and control the final level with a selig gain in the end of my chain. I rarely touch the device's input and output levels and use selig gain for this. Usually I'll set the initial gain so that each channel peaks at -12 to -18 DBFS and work my mix from there. I like to mix clean and I try to have a cohesive clean sound from the beginning.