An interesting idea, but I don't think it works out fully.

On Earth, life appears to have developed within a few hundred Ma of it being possible, and perhaps on a much shorter timescale of 1-10 Ma. This, in an Earth history of 4.6 Ga.

If conditions on planet X remained suitable for the encouragement of proto-life, then it seems that the transition to Life would be essentially inevitable. (if you're a betting man, odds of 50:1 to 5,000:1 seem likely from age ratios alone, and that's assuming a linear process, not a non-linear one).

If conditions on planet X did NOT remain suitable for the encouragement of proto-life, then it would fail and revert to pure inorganic chemistry.

After a few billion years of persistent arid sterility, global permafrost, and searing surface radiation, it's not likely that any organic traces of proto-life would remain, in my opinion.

Some relevant reading:-

"Life on a young planet" - Andrew H. Knoll
"The ages of Gaia" - James Lovelock
"Environmental Evolution" - Lynn Margulis et al.