I also am inclined to think that the story has undergone some "embellishment" over the years. In the WWI era, discharged soldiers were not allowed to bring their rifles home; further, the M1917 would have been a new rifle at the time, with every one desperately needed in France, so it is very unlikely that one would have been issued to a border patrolman, then deactivated and given to him.
For some years between the wars the Army sold 1917's through the DCM at a very low price. These were often purchased for use by military academies, drill teams, and school/college honor guards and deactivated so they would not be a danger in the hands of the youngsters.
The barrel probably is not salvageable (it would depend on how the chamber was plugged), but the receiver should be OK unless the heat treatment was ruined by welding.
As to what would have been issued to such units, F. Guffey may be correct; Krags were plentiful at that time and while some were used in training, they were not usable by the AEF. (To set the time frame straight, Pancho Villa - real name José Doroteo Arango Arámbula - raided Columbus NM in March, 1916, long after the regular army was equipped with the M1903 Springfield, but two years before the M1917 came into being.)
Without getting into too much detail, in response to the Columbus raid, Wilson sent General Pershing and almost the whole U.S. Army on a wild goose chase through the mountains of Northern Mexico; they never got anywhere near Pancho Villa, but the "exercise" did provide some valuable training and lessons that helped when the U.S. became involved with a more formidable enemy in 1917. The Mexican expedition saw the first combat use by the U.S. Army of motor vehicles, aircraft, and field telephones, to name a few innovations.
Jim