Short answer no - MODE switch takes in pure DC from the power feed from the POWER switch.
It can, if you get a severe clipping effort on the ALC control...affects the "noise level" the Pure DC arriving thru the MODE switch - telling you the MODE switch needs cleaning - the wiper to wafer contacts are dirty - leaving a resistive effect on the power Draw.
This can affect SSB mode, by how much, depends on how dirty the switch's' internal contacts are. The dirtier the switch wiper contact - the worse the voltage drop hence the noise appearing as power draw thru the power line to the Final and Driver. Would affect one mode over the other LSB or USB but unless it was submerged and found in a deep dive - like Jimmy Buffets old record collection - then suspect the switch.
Mode though - runs pure DC from the power supply feed - so do a continuity check from the TP stem, back thru MODE switch into thru the power switch to the Power supply wire at the Power Switch - check all modes for resistance in 1X setting.
Adding - only the AM mode would show higher ohmic reading of whatever value of the R193 - because R193 - a 220ohm 1W carbon composition resistor straddles the PNP - TR41 - the other modes draw straight thru from power supply/filter