Plant life typically decomposes and so it's carbon neural. I can't speak to the plankton, but I definitely want to look that up now, because 70% of the surface is water. That could be a big effect. I do want to point out that the carboniferous was unique though - microorganisms had not yet evolved to be able to digest the cellulose of trees. So there was millions and millions of years of trees growing, dying, and sequestering carbon. That doesn't happen anymore.
On the one hand I commend you for wanting to learn about the role of phytoplankton in carbon fixation -- if you don't know about it, what else might you not know? On the other hand I am disheartened that you confuse lignin with cellulose. It is lignin that evolved at the outset of the Carboniferous, and which fungi and co did not yet have the ability to break down.
