Correct, the Y-rated caps are responsible for EMI C-L-C or Pi filter bypass currents to suppress noise in each direction, by lowering impedance to FG but but too big a cap that it exceeds the IEC, UL safety leakage specs.
This one is rated at 47-63Hz 0.3mA.
As I recall the limit per PSU is 0.5mA and 2.5mA per commercial unit, which ay have multiple PSU's.
i should warn you that the downside of earthing secondary DC in SMPS is increased susceptibility damage in HIPOT tests. Factories will test unground secondary and pass and I discovered % catastropic failure in one source after they transferred production from SD to mexico . The causes were obvious to me with greater HiPOT stress before switching transformer, since the isolation in the transformer is now shunted. It took me a 1 lot reject to get the QA 's attention with Root Causes illustrated. This a product I designed and being assembled with 1k units/mo for Avaya/lucent.