Can there be interference problems when having two ADF5356 working in the same cavity and with different phases?

If there are two different signals which have a phase offset, constructive and destructive interference could occur, leading to waveform distortion.

Can two ADF5356 components be used to dynamically control and resynchronise the phases of two RF chains, with the phase of one oscillator adjusted relative to the other?

This design could introduce unnecessary impurities. These could be minimized by the use of one ADF5356 component as a master clock (PLL) which branches into two paths, one path that is unmodified and a second path which includes a digital phase shifter reducing the need for two PLL and two oscillators. The HMC1133 is one example of a digital phase shifter that could be used.