JZ and Nick,
I think there are two kinds of switching here. One kind occurs twice each RF cycle due to imbalance of the push-pull. Another kind is the keying envelope. I think Nick is talking about the first while JZ described the latter.
The "spikes" that could occur twice each RF cycle would have to be super brief and the spectrally at very high frequencies, so the #43 ferrite cores, windings, stray caps, CDS of the MOSFETs, etc should attenuate them considerably.