Once gone, things get very serious.
The amount of energy that melts a tonne of ice at 0 C to a tonne of water at the same tempreture will raise that same tonne of water from 0 C to over 79 C.
ie. Energy going to melting ice isn't going toward raising sea and air tempretures .. once there is no ice to melt that same energy will direct itself toward cooking things up.
A lot.
The much more important effect of losing polar ice is the albedo effect, that is how much solar radiation is reflected back into space by ice and snow vs how much is absorbed by exposed ground.
Just in case: losing ice in the polar oceans also doesn't increase sea levels (since floating ice has less volume than the water it floats on), but losing ice that lies over land, such as in Greenland, directly contributes to rising sea levels.
Losing the albedo of floating ice has the same effect on warming as does losing snow or ice on land.
Furthermore Milankovitch cycles induce mild climate changes but climate changes don't "lead to milankovitch cycles" . . .