Is there 'no actual equilibrium'?
Yes there is actual equilibrium. The Achilles and the turtle kind of argument fails for three reasons, one of which you mentioned yourself:


Like you said, the number of molecules is finite, so the matter is not infinitely divisible; there must be a limit.
More importantly, nobody really cares about one molecule. Anyway, it's not like the system is going to hit just the right number with one-molecule precision. No, there are going to be mighty fluctuations involving millions of molecules, and they never stop (that is, unless you freeze the system down to absolute zero, in which case reaching the equilibrium may indeed become problematic). Like anything with molecules, equilibrium is a statistical thing, and once we're within certain error margin from the theoretical figure, we might just as well consider the goal achieved.
We may circumvent the argument altogether by playing with the conditions. Say, we want to get a saturated solution of some salt in water, and it just seems to take forever. But wait, what if we just heat the thing up a bit (which would make the solubility go up), dissolve the exact amount we need, and then cool it down again? Here is your saturated solution in a finite time. You may even make it supersaturated if you'd like.