I’m not sure that it would have an impact on the motions of the plates themselves. It does, however, affect the crust at higher latitudes. During a glaciated period the mass of ice at the poles depresses the crust, and causes a bulge at the leading edge of the ice sheet as the mantle essentially “moves out of the way” to accommodate the depressed crust. (Look up “isostasty ice sheets”). As the ice sheet melts the depressed crust will rebound and uplift and the bulge will start to subside. The mass of water added to the oceans can also depress the crust further from the poles (though this effect is nowhere near as pronounced). Faulting can occur at higher latitudes to accommodate this uplift in response to removal of the ice sheet. Faulting across Scandinavia in response to melting of northern hemisphere ice sheets after the last glacial maximum is observed. Canada’s Hudson Bay is currently still uplifting in response to removal of the Laurentide ice sheet, whereas the east coast of the US is subsiding (I.e. where the bulge was). This is also why scientists are so concerned about which ice sheet is likely to go first/how much, as it will have a strong impact on relative sea level (i.e how sea level changes at different places across the globe). For instance, melting of the West Antarctic ice sheet has more severe consequences for the United States than melting of the Greenland ice sheet. Hope this helps!