"Far more worrying is side-slipping"
Why is this more worrying?
Significant intake disruption 'might' lead to compressor stall.
Examples around for example I recall the early 747's (think GE engine varients but cant remember), were vulnerable during strong x-wind take offs. CFM 56 is much less suseptable but guess its possible.
I would be concerned about this problem during a significant side slip (...as opposed to forward slip).
YM.