No, it won't. Plants will continue to absorb mostly potassium. Caesium is absorbed in very, very small amounts.
What "huge amounts" of caesium are you talking about? Caesium is not poisonous. Total inventory of caesium, all isotopes combined, in the fuel on the whole F1 site is on the order of 100 kg. Its danger comes solely from its radioactive isotopes, not chemical/biological effects.