I use the Acustocom 2 because I think it has a good bandwidth (0.2 to 8.0 GHz) to detect EMI with potential biological effects.
My opinions of LEDs in general: As I understand it, the problem with LED lighting is the power conversion step: from 110 VAC to the lower DC voltage required for the specific LEDs. Also, properly-designed LED drivers are current controlled (not voltage controlled), so that can also add noise to the signal from the feedback loop in the current control circuitry.
But if you drive the same LEDs from a quiet (DC with no EMI) source, such as a battery, I do not think the LEDs themselves emit any EMI.
I know this partly because I have developed some extremely sensitive scientific instruments based on electro-optics (LEDs), and I was able to achieve and verify by measurement that when you use a quiet power source, the noise emitted from LEDs was essentially zero.
Keep in mind: I am not an LED expert, so this is just my semi-informed opinion.