No, because ordinary explosions do not cause significant earthquakes, and the earthquakes are occurring in places and at depths where tunnels are almost impossible to have been dug.
First, we have extensive, public information about seismic activity across the United States, published by the U.S. Geological Survey and other non-federal entities. The U.S. is covered by a network of thousands of seismographs, including more than 400 through the USArray program, providing a rich set of data for any seismic activity within the country.
"Each USArray station includes the instrumentation necessary to
continuously sense, record, and transmit ground motions from a wide
range of seismic sources, including local and distant earthquakes,
artificial explosions, volcanic eruptions, and other natural and
Each type of seismic activity generates a distinct fingerprint. For example, we can tell the difference between a nuclear explosion and a non-nuclear explosion of equivalent size by the relative abruptness of a point-source blast compared to a volume of explosives. There's a difference between strike-slip activity on a deep fault and a series of demolition blasts and the subsequent collapsing rock of tunnels.
Also, according to the U.S. Geological Survey, "even huge amounts of explosive almost never cause even small earthquakes, and it would take hundreds and thousands of small earthquakes to equal a large one, even if it could be done."
In the particular case of South Carolina, some of the quakes in the recent series are occurring from 500 meters to 5 kilometers deep about 1,200 miles from the Mexican border. The deepest smuggling tunnel between the United States and Mexico went to only 27 meters, and most cross-border tunnels are less than 10 meters deep, in part due to the high groundwater table. The typical groundwater table for Kershaw County, South Carolina, where Elgin is located, is about 53 feet, or 16 meters, according to the USGS.
It is unlikely that any smuggling tunnels being demolished would be below the groundwater table at the depths of the detected earthquakes, and unlikely that any such demolitions would cause earthquakes.