Can a paramterized class react to parameters outside of itself?

Param
5

Yes. But how depends on your specific use case. An example is

import param

class A(param.Parameterized):
    value = param.Integer()

class B(param.Parameterized):
    a = param.ClassSelector(class_=A)
    value = param.Integer()

    @param.depends("a.value", watch=True)
    def _update_b_value(self):
        print("updating from", self.value)
        self.value += self.a.value
        print("updating to", self.value)

a=A()
b=B(a=a)

a.value=5

$ python 'script2.py'
updating from 0
updating to 5
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