No they couldn't
The energy necessary to lift either Phobos and Deimos from Mars and place them into orbit is far larger than the amount of energy necessary to vaporize them. Planetary ejecta is size constrained, and those constraints have been established in detail.
Another hypothesis is that the force from a larger impact stopped smaller fragments from impacting. But there are no indications on their surfaces that this may have been what happened.
Thus it seems that simple capture by gravity was what occured. I believe it has been calculated when Phobos and Deimos will ultimately accrete with Mars, os it seems likely that that calculation could be run in reverse through time to analyze their capture.