No, it will completely eliminate it, if the capacitor is large enough. If you're super paranoid you can do the maths and compute how much does it cut off at such frequency ranges. It's likely to be a ridiculous value. And one does not have an infinite amplitude resolution in any measurement device.
Also, you can just power the LED from a separate voltage regulator. Which is somewhat likely anyways, as the IC will probably want a lower voltage.
(Don't get me wrong, it's cool stuff, but there's also a very easy solution.)
It's a harder EE problem than you think. For example the Samsung Galaxy S8 was attacked by analyzing video footage of the power LED of Logitech Z120 USB speakers. Those were most certainly on a different power supply and the two were connected by a long wire.
There are circuit level solutions but the solution is not a $0.01 MLCC.
And once you solve the LED problem remember: The S8 was attacked by plugging in a peripheral to it’s 5V USB supply. Imagine if the peripheral was instead a high speed ADC that just measured 5V USB directly…
Also, you can just power the LED from a separate voltage regulator. Which is somewhat likely anyways, as the IC will probably want a lower voltage.
(Don't get me wrong, it's cool stuff, but there's also a very easy solution.)