Jay Melosh, Blitzer Award Winner says it's possible.
"The mechanism by which large impacts on Mars can launch boulder-sized surface rocks into space is now clear," said Melosh, who is considered one of the world's foremost experts on impact cratering and the importance of extraterrestrial impacts in shaping life on Earth.
"Both theory and direct measurements on some of these rocks tell us that living microbes could have survived both the launch and travel in the vacuum of space for periods long enough for them to have arrived intact on the surface of our planet," he said.
The reverse journey of surface rocks launched from Earth and landing on Mars is likewise possible, he added.
"Research at the UA and elsewhere has filled in many details of this process. Biological exchange between the planets of our solar system seem not only possible, but inevitable," Melosh said.
I share his sentiment.