I'm going to answer your general inexact question with a general inexact answer. The consensus is that LTP is correlated with learning.
To clarify in more detail, studies have shown that when an animal performs a learning task that involves the hippocampus(which is important for memory), and the animal effectively learns, less LTP is seen in-vitro in brain slices from these same animals. LTP is said to be occluded or blocked since potentiation of those synapses have already maximized through the in-vivo mechanisms. This can be interpreted as learning affecting LTP or at least both acting on the same basic mechanisms of the synapse(strengthening and weakening).
See for ex.
Learning induces long-term potentiation in the hippocampus.", Jonathan R Whitlock, Science (New York, N.Y.), 2006;313(5790):1093-7