Compute my Sacred Geometry
Python 2.7, 285 bytes



from itertools import*
from random import*
def f(s,r):
 p=[];n=1;k=1;P=1;d=choices('123456',k=r);D=permutations(d,r);O=product('+-*/',repeat=r-1)
 while-~s*3&gt;n:p+=P%k*[k];n,k,P=n+P%k,k+1,P*k*k
 return any(n in{eval('int(%s)'%'%s'.join(i)%o)for i in D for o in O}for n in p[-4:-1])


Technically conforms to the specifications of the challenge. Only returns True/False, does not expose the dice rolls used or the expression used to caller.

Also, this algorithm ignores grouping, since we can perform the same operations without grouping by using ordering instead. (This would not be true if exponentiation was one of the possible operations, for example.)

Exponential runtime, since it generates all possibilities and then checks if at least one solution exists.