It wouldn't remove them. You'll just start developing the characteristics from the champagne yeast for the rest of the fermentation, leaving the character already created.
Yeasts produce flavor compounds as they ferment. The more they ferment, the more flavor compounds they will produce. So if this batch went, say, 2/3 of the way on the first yeast, there'll be something like 2/3 of the yeast character you would have gotten if it had fully fermented. Then you put in a champagne yeast, and that ferments a little and accordingly leaves a little of its character (which is fairly neutral, and so likely won't interfere).
British brewers used to do this to barleywines; they wanted the flavor from their normal yeast strains, but they weren't strong enough to finish the job. So when fermentation stalled, they added champagne yeast to dry it off.