Yes, it's possible to connect one side of the secondary to earth.
No, it won't trip the RCD.
RCDs work by sensing the difference in currents between the phase and neutral conductors. There's no way, a fault on the secondary side of a transformer, can trip an RCD connected to the primary side. The exception being an autotransformer, which is irrelevant in this case.
The only way to get RCD protection on the secondary side of the transformer, is to earth one side of the secondary and put another RCD after it.
A 110V transformer with one side of the secondary earthed and no RCD, is arguably more dangerous, than 220V, with no an RCD.