The copper don't even need o be too close to have significant impact on the board; A long time ago I was assigned to solve a serious problem on an ECG signal acquisition board. Although it had a well distributed GND plan on both sides, and despite there were analog filters, and even other engineer have made an attempt to elliminate the artifact by digital filtering, it still had a strong presence of noise in the printed waveform. The first solution I presented was to place a copper plate between the equipment chassis and the PCB, but it did not work, even moreover worsening the signal quality. The 2nd solution was to just ground this plate to the GND of the board, and Bingo, the noise disappeared. The learning I gained from this experience was that any floating metal object in the nearness of a net can accumulate/reflect electrical charge from the nearby EM source, particularly if its circuit has high impedance paths; therefore, Yes, floating copper can destroy the signal integrity, sometimes it is more appropriate to remove them than to keep them there, specially if overall ground copper plane clearance is short.