[morzh]

Rod

Two Y-caps make sense if you use them from L/N to the chassis; this is only makes sense in the transformer radios with the chassis being common GND.
Especially if the chassis is grounded to the actual Earth GND.
Y-caps are used to filter out the Common Mode type of noise. This is typically RF type, when both L/N act as one antenna (have the same voltage on both). They are usually smaller value types (there are large ones, in hundreds of nF, but used in other applications).
A Common mode chokes are used for the same purpose, often in conjunction with the Y-caps.
Because the noise is CM, putting a cap of whatever value between the L and N will not help with this part of noise, as there is, well, nothing to conduct.
And even if you think the N is Earth, in fact it is not quite it, as it has the same noise as the L.

What I have is an X-cap. The X-cap (we went through it before, as to where it is used, I am repeating it to make the picture more detailed) is used across the L/N and not from L/N to the chassis/GND.
As for the purpose of it, it is used to filter the Differential noise. That is the one mostly made by conducting currents. Because it is differential, the cap will happily conduct the noise from L to N, and so this part of noise will be routed away from your device.
Because often times the frequencies of the noise go quite low, the value of this cap is picked to be quite a bit larger than the Y-caps;' it is often between 0.1uF to a few uF. It also works well with the differential inductance, that is those place in-line with L (or L and N but uncoupled from each other); this forms one-pole LC filter. Sometimes the leakage inductance of the CM choke (which is differential in nature) is relied upon for this part.

So, in my radio (AC/DC) due to the absence of a separate isolated chassis, there is no reason to have a Y-cap.
In a transformer radio, there is.
Better yet, there is a reason to have both, same as they do in today's off-line SMPS (Switching Mode Power Supplies): two Y-caps to the chassis, whether it is connected to the PE or not, and one X-cap across the AC Line. I would go with 10nF for Y-caps and 0.1-0.3uF for X-cap.
If the X-cap is placed before the Power Switch, use a 2M bleeder resistor to drain the charge when the radio is unplugged.

Coming back to two Y-caps making one X-cap: yes, it will, but it will be a bad X-cap, as it is small in value (2x10nF make 5nF X-cap, which is not much).

And the last note: in today's devices the function of the input filter is opposite to the one in the old radios: in the latter it protected the radio from the interference via the power line; in the former, it protects the power line from the device.
But the filter remains largely the same.