On this Lonely Speck page, they show how ISO invariant the X-T1 (and very likely the X-E2s) is. As such, there’s no benefit in terms of signal-to-noise ration to shoot at higher ISO. As I understand it, you can shoot at ISO 200 and push the EV in post, with the same result as a 6400 ISO shot unpushed. You just get lower dynamic range as you increase ISO.
At higher ISO there’s an amplifier voltage boost, and maybe this boost can add some noise visible at longer exposure? (though I don’t know if this boost is applied during the whole light gathering process, or only at the end when converting the image).
I actually tested this with the XE2s and found that noise increased linearly up to about 1600 then “jumped” at ISOs higher than 1600 (this is why I typically don’t shoot above 1600 anymore). The reason for increasing ISO while shooting has more to do with brightening the live view image but I think there’s also some “Fuji secret sauce” involved because the higher ISO images still look better than the lower ISO images that have been pushed.