Panspermia of this type is certainly feasable, and I suspect that if there is any life in our solar system besides earth it probably originated in the solar system.

But although interstellar panspermia is certainly possible, it may not be necessary; the circumstantial evidence is that life has arisen idependently in many places in the past, and will continue to do so in the future. We'll never know for sure until we start sampling biological material from outside the solar system. If it all arose in one place, it will be chemically very similar.

Frankly, I prefer a universe where life arises naturally over and over again to one where it has an origin in one place only. I prefer the principle of mediocrity, I find it much more reassuring than DNA exceptionalism.