What does (PNP) BJT with shorted C-E do?
From the 1980 National Semiconductor Linear Regulator Handbook, section 7.1.3 has a High Current Regulator with Short Circuit Limit During Output Shorts, in an identical layout, but with Q2 being a simple Diode D.


This current boost circuit takes advantage of the internal current limiting characteristics of the regulator to provide short-circuit current protection for the booster as well. The regulator and \$Q1\$ share load current in the ratio set between \$R2\$ and \$R1\$ if \$V_d = V_{be}(Q1)\$
\$I1 = \dfrac{R2}{R1} \cdot I_{REG}\$
During output shorts
\$I1(sc) = \dfrac{R2}{R1} \cdot I_{REG}(sc)\$
If the regulator and \$Q1\$ have the same thermal resistance \$0jC\$ and the pass transistor heat sink has \$R2/R1\$ times the capacity of the regulator heat sink, the thermal protection (shutdown) of the regulator will also be extended to \$Q1\$. Some suggested transistors are listed below.
The minimum input-to-output voltage differential of the  regulator circuit is increased by a diode drop plus the Vr1 drop.


Considering the identical layout, and NatSemi being the source of the layouts, the shorted Q2 PNP C-E will act the same. As @Robherc suggests, it's likely used as a matched pair, to provided some performance gain compared to a random diode which would have a much different performance. Unmatched, I suspect the different IV curves can lead to over or under current conditions, or too much cycling/oscillation. Of course, given that the application note suggests a diode, that's probably not the case.
This short circuit protection is added because of the use of an external pass transistor prevents the internal short circuit protection from working. It could just be omitted, if short circuit protection is not needed.