This seems to me pretty obvious, There is not but I might be leaving a special case. As I see it 1SAT (only one literal per clause) and 2SAT can be easily transformed into 3SAT. An any clause with more than 3 literas has been proven it can be transformed into 3SAT. So maybe the question should be asked as: Do all boolean algebra can be put into SAT? or can we define boolean algebra with ony these operators? AND OR and NOT
Is there any boolean algebra expression that can not be put into 3SAT?
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No, there is not.
I will not give the full proof but here is the main idea: Write the given formula in a normal form i.e. conjunction of disjunctions. Use induction on the number of variables on an expression. Pick the longest subexpression with n+1 variables, introduce a new variable for some part of subexpression to leave an expression of n variables, add the constraints for the new variable to the formula, repeat the procedure as many times as needed to have a formula where the longest subexpression has n variables.