Theoretically, yes. You've summarized it well, and I agree with MrTeo:. However, if you're trying to think practically, there are other things to consider. Putting it simply, as the reaction proceeds, the limiting reactant becomes harder and harder to find, mixed in with products and other reactants. Getting more nitpicky, you'll have to consider how well it mixes, what volumes we're talking about, how rapidly it reacts ... and a host of other things, like vessel size and shape, loss of one or another reactant by various means, and other things. So we often do't accept that a reaction that "goes to completion" is guaranteed to have zero reactant left over.