By 'Deep Learning' I'm referring to the current (around 2015) well-publicized designs being pursued, such as convolution and recurrent networks, and similar approaches.
What do the key proponents of this technology say? I'm not aware of a single high-profile Deep Learning researcher who claims that DL will, by itself, lead to AGI (as defined above). In fact most of them go out of their way to state that DL cannot pose a serious danger because of its inherent limitations.
Here are some of the essential AGI abilities that the majority of DL systems do not have:
Now, this is not to say that DL combined with other techniques or frameworks cannot overcome these limitations, but then it isn't DL = AGI. Several AGI researchers believe that some form of DL technology will be an important aspect of AGI -- perhaps forming part of a comprehensive cognitive architecture.