I’m going to guess no - if it takes a year to get there even through the Gate then we must be looking for at least double that for return messages. And unless they’ve cracked quantum entanglement radios, which don’t care about distance, any conventional signal is looking to travel something of the order of millions of light-years - which needless to say would take far too long even if they could generate a signal ungodly powerful enough to be picked up at that distance.
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