My advice would be to open it up to see what's inside, before even thinking about 'scoping the output. It's possible the mains is already clean enough where you live, that there wouldn't be much difference any way. By reverse engineering it, you can figure out whether this device will actually make any difference or not. No doubt other, much safer tests which can be done, to see if it works, without connecting it up to the mains and connecting a 'scope to the output. For example, connecting a signal generator to the input and a load resistor to the output, sweeping the signal generator from the mains frequency, up to a few MHz and 'scoping the output, will tell you how well it filters RF, without having to worry about dangerous voltages.
When ever something is marketed at improving audio, it always makes me feel more cynical. Mains power filtering is very real and a very noisy supply can cause problems with audio. as well as other equipment, but most of the time it shouldn't be a problem. I'd be more inclined to buy a decent brand mains EMI filter and put it in a box with sockets and a mains cable, rather than buying anything like this, which could just as easily be overpriced rubbish as a decent product. However, I'll remain open minded about this device, until I've seen the insides or the results of prpper tests.