If done improperly, can a transvaginal ultrasound cause a perforation which could result in free-air in the abdomen?

In theory only: have never seen or heard of it in over 30 years. perhaps if ultrasound was done shortly after a hysterectomy and opened the cuff. would think it would require considerable force.

Not likely: Free air in the abdomen usually represents a perforated bowel and can constitute a surgical emergency. However, there are non life threatening causes of free air. In Italy, they use a technique of injecting air and saline into the uterus to test patency of the fallopian tubes. This could cause free air. A standard diagnostic ultrasound should not.