Can a transformer be placed next to RF module?
Radiated noise depends more on household devices that use triacs or SMPS circuits without PFC. If any Op Amp line connected circuit had high impedance with a large loop circuit between ground and neutral, it could pick up noise like an antenna.

I do not see an issue with your AC transformer without more details. Ground could be used as a shield and any external data ought to be opto-isolated or properly designed serial port. If just using an RF Tx, take care on supply and return noise with suitable filters.  

You do not want to connect neutral to ground and generate ground currents, other than a noise suppression caps to ground with 0.5mA leakage max total , if used. The RF transmitter should have good immunity from radiated 60Hz if low impedance inputs, but conducted noise must be eliminated.
Your ground path must be carefully designed, whether it is neutral or gnd. Common mode chokes do well to suppress external conducted noise coming in.