No, no it really hasn't. It has relied on the ability to make predictions based on pusblished theories, methods, laws etc. Even for hard-science experiments it's not even clear how you could record all the required knowledge to replicate an experiment. Every configuration, every machine, every particle in the air, every bit of software.
I really wish people engaged more with the actual history of science instead of what they believe it to be.
edit. To give a little more meat to my rant here's a good reading (https://plato.stanford.edu/entries/scientific-reproducibilit...):
"If replication played such an essential or distinguishing role in science, we might expect it to be a prominent theme in the history of science. Steinle (2016) (...) claims that the role and value of replication in experimental replication is 'much more complex than easy textbook accounts make us believe' (2016: 60), particularly since each scientific inquiry is always tied to a variety of contextual considerations that can affect the importance of replication. Such considerations include the relationship between experimental results and the background of accepted theory at the time, the practical and resource constraints on pursuing replication and the perceived credibility of the researchers. These contextual factors, he claims, mean that replication was a key or even overriding determinant of acceptance of research claims in some cases, but not in others."
The history of replications is extremely nuanced. Empirical results and by extension replications are one line of argument in scientific discourse, but by no means the only one.
I personally hold that valid predictions in the context of interesting problems are where it's really at. In the "Structure of Scientific Revolutions", Kuhn argues that at some point paradigms cannot make THESE kind of predictions anymore. Revolutions do not happen because of failed or missing replications.
Therefore, stating science "has relied on replication" is historically and epistemologically false. It's also misleading because the replication crisis happens due to a lack of theory and misguided incentives, not because some discipline has left the holy path of finding truth.