I wouldn't make that swap - save it for when you get your hands on an amp that's designed for the 5Y3... (note that I doubt you'd do any damage, but no good point).
So long as you're using the same type rectifier, I'd say it will affect tone BUT it's in the lower tier of things that matter. Why it can affect tone has to do with subtle changes in voltages, which affects how the tubes are biased, which can subtly affect your tone.... small time differences within the same rectifier types. But once you start considering different types - solid state vs 5y3 vs 5u4 vs GZ34... they can somewhat more substantially change the behavior of the amp. They're NOT necessarily interchangeable in any given amp, so do your research before swapping.