awk supports this:
awk \'{print $(NF-1);}\'
but not for user-defined variables:
awk \'{a=123; b=\"a\"; print $($b);}\'
The $ notation is not a mark for variables, as in shell, PHP, Perl etc. It is rather an operator, which receives an integer value n and returns the n-th column from the input. So, what you did in the first example is not the setting/getting of a variable dynamically but rather a call to an operator/function.
As stated by commenters, you can archive the behavior you are looking for with arrays:
awk '{a=123; b="a"; v[b] = a; print v[b];}'