Short protection, yes; but you need to get there first!
This is a special case of a more generally known circuit, the foldback current limiter.
Obviously, this is not brown-out protection (i.e., against a moderately heavy -- not shorted -- load), and peak output current will still be hFE limited(!).
There are more clever ways to solve this problem -- that is, current sense without shunt. Monitoring the pass transistor's Vbe for example, usually as part of a dissimilar matched pair. This is hard to do in a discrete circuit, of course, and notoriously hard even in an IC, as the current limit ratings of many LDOs can attest.
Tim