Loved this post. However, I don't completely agree with the point that natural selection is must for it to have "life". Let's just assume a arbitrary self sustainable and reproducing entity. It doesn't have to be typical biological cell. But what it can do is get components from environment to promote its own growth and make copies of self. Now, selection here will arise by default.
Let's say this arbitrary entity was surrounded by molecular components it needs. Let C be concentration of these components. Then change in concentration of these components will be inversely proportional to copies produced by entity. As can concentration decreases so will the proliferation.

Now, if with time this entity do not comeuppance with ways to lie dormant until it finds a new source, or active forage for source it will just degrade by basic laws of thermodynamics. So if entity doesn't cope with environment it's extinction is inevitable, however we classify it. One way of coping with environment is to make a lot of copies let there be errors. (Maybe God should have said let there be errors, instead of let there be light). If rate of error is too high it will face extinction again. But at certain threshold of errors this will generate adaptive radiation. So in case of environment change probably one in million copies of this entity will survive and give rise to its copies.

So selection pressure and ability of entity to respond to it is a predictor for how long will it self sustain. A day or a million years. Nevertheless, IMO, that should not rule out self sustaining entity highly prone to going extinct under small change in surroundings.

Protocells made till date lack ability to self sustain without an artificial system to provide them with nutrients. A lot like virus. It has stuff it wants to replicate, but not enough machinery to do it. It's sustainablity depends on coming in contact with a host and infecting it.

Nevertheless, this is good stuff. Looking forward to read more of it.