If the polar ice melts revealing the soil, would ancient plants flourish again?
First, most polar ice is over the water. There is plenty of ice on Greenland, though, so let’s discuss that.
To have undisturbed soil under a glacier with plant seeds or other biologic material preserved, you’d need a very gentle environment. The bottom of a glacier is about as far away from a gentle environment as you could possibly get.
Glaciers are massive rock-grinding machines that rip apart the surface over which they pass.
Ice sheets can remove hundreds, even thousands of feet of rock as they pass over, depending on the size of the ice sheet and the length of time it exists. There are several types of glacial deposits, but they are mostly composed of boulders torn from the ground, pebbles, sand and clay- the grinder breaks down rock at every level.
Surfaces over which glaciers pass are always scraped clean. Literally scraped. Glacial striations on rock surfaces are common features.
So, even if there were a chance that some of the original soil might remain behind, there is no chance of biologic material surviving these geologic grinders.