In short, no.
Let's see what is a monad? This is a data structure that has two pure and bind operations:
pure(v) - getting monad for value v
bind(f) - execution of the function f , which takes as its argument the value of the monad. returns a new monad.
The following rules should be followed for this structure:
Left indentality
pure(v).bind(f) = pure(f(v)) applying the bind operation on a monad is equivalent to creating a monad from the value of the function f with argument v
Right identity
pure(v).bind(Monade::pure) = pure(v) applying the bind operation with the pure function to any monad is equivalent to the same monad.
associativity
pure(v).bind(f).bind(g) = pure(v).bind(g(f(v))) sequential use of bind operations with functions f and g on any monad is identical to using bind operations with the composition of these functions on this monad.
Now, if you look at the builder pattern from the point of view of these rules, you will see that it does not have operations that satisfy these rules.