One of the most important roles played by bacteria is the fixation of nitrogen. Biological nitrogen fixation is carried out primarily by bacteria. There are no known plants that express nitrogenase type enzyme. So plants cannot fix nitrogen.
Without bacteria in the ecology... the ecosystem is in trouble from nitrogen starvation.
That said, denitrification, the removal of fixed nitrogen and conversion back to nitrogen gas is also catalyzed by bacteria. So no bacteria, no lost of nitrogen by biological means.
Nitrogen can be fixed by lightning discharge. About 5%-8% of all nitrogen is fixed this way http://www.biology-pages.info/N/NitrogenCycle.html. However lightning does tend to cause forest fires... which results in the lost of nitrogen.
So where does that leave us? We will have to guess how much nitrogen is lost from forest fires (and burial by sedimentation) vs gain from lightning discharge.
That is is not at all easy to guess. In a world of high rainfall (lots of rain forest)... you can have plenty of lightning and no fires. But a world of swamps would have also plenty of organic matter (and nitrogen) being lost through sedimentation. A drier world would have more fires.
If anything... I would guess that such a world is unstable in the long term, certainly on a geological time scale. Eventually the environment will change to one where nitrogen is lost, and fixation by lightning is reduced... and the ecology will collapse from nitrogen starvation.
Could bacteria emerge in the world?
My guess is no. A second abiogenesis event is unlikely to occur when life is already present. The plant alive on your world would prevent any new form of life re-emerging. Plants are not quiet neighbors minding their own business. Plants secrete toxin to poison other plant. Limit growth. (Walnuts are a great example) Plant root do absorb simple sugars and amino acids. Example. http://link.springer.com/article/10.1007/BF02202082 So the raw material for new life will not accumulate.
That said... there is no reason why plant life cannot simplify itself to a single cell... such extremes have happened to parasitic barnacles of the Sacculina genus.. which look less like a crustacean (ie crab) than barnacles normally do and more like fungus. https://en.wikipedia.org/wiki/Sacculina
So we could have single cell plants.. descended from higher plants.
What is uncertain is if plants could re-evolve an enzyme to fix nitrogen. Nitrogenase (nif) appears to have evolved once in methanogens and by lateral gene transfer was moved to many other bacteria. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3733012/#B7