I designed a mains harmonic "filter" that was effectively a voltage source in series with the mains to make the mains signal pure. The heatsinks of this internally ran at mains (240V) all the time. The whole circuit was therefore sitting on the live all the time. Needless to say I had warnings all over everything that the whole circuit was live.(Silk screen text on the pcb as well as sticky labels on everything! In this case I had no choice because I needed to make it so that the box could be used on a three phase system, hence I couldn’t interrupt the neutral.
Since your whole circuit is at the same potential there should be no problem. You would only get an issue if there were to be some high impedance node in your circuit capacitively coupled to the case. The earthed case would act as a capacitor with 110V across the plates. If a high impedance node in your circuit were to couple strongly with the case then you might get a problem. The coupling from a wire to the case would be of the order of 10pF to 100pF, but no more than that. You should be able to work out if that much capacitive current flow would cause a problem to your circuit.
I get 100pF as 32Meg at 50Hz. Suppose you had a low power switch circuit using a 1Meg pull-up and no capacitor. You would get about 110/33=3V RMS on the open switch, which would probably cause a false reading. Just think of injecting a 100pF capacitor with 110V (relative to your circuit) on any nodes that are connected to wires or large pcb lands. That will tell you which parts of the circuit might be susceptible to problems.
