The ground pressure would not, I think, be insurmountable - it's got an area of 490 square metres, so it's only about two tonnes per square metre of horizontal area.
If the treads are 1/2 the width of the vehicle (as per the design), it's got a ground pressure of 4 tons per square metre - which is 0.4 kg/cm2. That's less than half that of a Tiger tank.
So it wouldn't necessarily destroy the roads it went on.
The bigger problem is that it has real trouble going through tunnels or over bridges of any kind - though with a 11m height it was just meant to ford, helped by the ground clearance that would let it drive over a standing man.
However, there is a problem in the calculations I've just given.
They assume the P-1000 weighs 1,000 tonnes. And that's nigh impossible.
The intended armour thickness was 10 inches on the sides. Assuming no armour on the roof and floor, and nine metres of armoured side (base to roof), that gives us four armour plates - two 10x14m and two 35x14m - and a thickness of .26 m.
Total armour volume= (2x45x9x0.26) = 210 cubic metres of armoured steel.
At 7.8 T per m3 for rolled steel, the armour alone thus comes to a rough estimate of 1,642 tonnes. Even if this is cut down by the form of the tank, it's very hard indeed to see the whole tank (complete with 20 tonnes dry weight of engine, for example) coming in at 1,000 tonnes.