If you were to fly an ILS in a knife edge would you receve GS and LOC be flipped?
No, the directional part of ILS is located at the ground. (Ground) transmitter creates lobes with specified frequency and modulation to mark the high, low, right and left areas.

LOC and GS signals are distinguished by the carrier frequency, deviation from the optimal approach by relative intensity of 90 Hz and 150 Hz modulation in the signal. These signals provides information about position relative to the airport regardless of airplane attitude.

So flying knife-edge LOC axis of the instrument still shows (correct) horizontal deviation and G/S axis correct vertical deviation.

Of course, display of the instrument is turned 90° together with the whole airplane, so its G/S axis now lines up with the green-blue boundary you see behind your windows (I hope you are not flying such maneuvers in IFR conditions :) ) but it is still the G/S axis and it shows vertical deviation from the optimal glideslope.

Only difference would be that airplane antenna won't match the transmitter polarization (ILS transmitters transmit in horizontal polarization and receiver is likely polarized in the same plane), so you loose some signal intensity and receiver can be more sensitive to reflected signals, therefore reducing maximal working range and possibly increasing probability of spurious signal detection.