It depends on the EV and how things are implemented, but, typically, yes. Is it something you'll notice in daily operation, almost certainly not - and if you do, you probably don't care about range/tire life/etc, because the only way you'll notice it is hammering on it, "wide open," (yes, I know there aren't throttle plates) constantly.
A typical EV is using, for quirks of history I don't fully understand, a 96S battery pack - 96 lithium cells in series. Fully charged at around 4.15V/cell, this is almost exactly 400V. Drained, around 3V/cell, you're closer to 285V.
In general, power electronics don't care about voltage - they care about current. And you'll find the limits on a controller are current based. This means that as the pack state of charge drops, at a constant current, you get less actual power out (because the voltage is lower).
So, if you're a Tesla with a bunch of the performance options, you might have a cap of 1500A out. Fully charged, ignoring voltage sag (which will be a thing at this sort of amperage), you're around 600kW delivered. Drained, call it 300V, that same current only gets you 450kW. And, if I'm not mistaken, the Teslas are significantly slower on a drained pack - if and only if you're asking for maximum performance. They can also warm the pack to reduce the internal resistance to deliver more voltage at a given current.
Now, in daily driving, does it matter? No. And I've never noticed anything of the sort on our Volt either, but then again, I don't go timing maximum performance 0-60 or quarter mile times on... well, ever, these days.
