Simpler way to run a generator function without caring about items

One very simple and possibly efficient solution could be

def exhaust(generator): all(generator)

if we can assume that generator will always return True (as in your case where a tuple of 2 elements (success,table) is true even if success and table both are False), or: any(generator) if it will always return False, and in the "worst case", all(x or True for x in generator).

Being that short & simple, you might not even need a function for it!

Regarding the "why?" comment (I dislike these...): There are many cases where one may want to exhaust a generator. To cite just one, it's a way of doing a for loop as an expression, e.g., any(print(i,x) for i,x in enumerate(S)) - of course there are less trivial examples.

Setting up a for loop for this could be relatively expensive, keeping in mind that a for loop in Python is fundamentally successive execution of simple assignment statements; you'll be executing n (number of items in generator) assignments, only to discard the assignment targets afterwards.

You can instead feed the generator to a zero length deque; consumes at C-speed and does not use up memory as with list and other callables that materialise iterators/generators:

from collections import deque

def exhaust(generator):
    deque(generator, maxlen=0)

_{Taken from the consume itertools recipe.}