Deep Learning is a subfield of Machine Learning, which is a subfield of AI, which is a subfield of AGI. Deep Learning is simply one small ingredient in the very large complex puzzle of AGI.
The question can be posed to the current popular implementations that focus deep learning on convolutional neural network techniques, rather than other possible implementations. Personally, I believe that this specific implementation is a dead-end when it comes to its ability to achieve human level machine intelligence by itself. But, I also believe that those working on it should passionately continue working on it. They will discover new questions and find new answers that we will not know about unless they continue their work. How much of it is useful for a true AGI solution cannot be known until the dust settles. However, it is very likely that some of the work done in even the current specialized focus of today’s popular deep learning implementation will provide useful insights up the hierarchy to the AGI solution.
So, the two are not mutually exclusive. In fact, Intelligent Artifact's AGI includes (non-CNN) deep learning functions.