@Tunk,
Yes, but that LM317 circuit is questionable in other areas. e.g. if the regulator is fed from a rectifier with no other loads, D3 is redundant, but as it has a significant value capacitor between Adj and ground, it *should* have a normally reverse biassed protection diode across R1, to prevent regulator damage if the output is shorted.
Also, with that decoupling capacitor on Adj, one has to consider whether the transistor will be transiently outside its SOA if wiper contact is lost. Worst case, it could have up to 28V across it with 5.7mA of base drive, which, allowing for hFE dropping with increasing collector current, could result in a transient peak dissipation in excess of 3W.
@GlennSprigg,
That's only effective if the circuit (and any load) can tolerate the pot going to max. resistance. As others have stated their experience above, if not, it can get expensive! IMHO, in most applications, linking the wiper to one track end does little except strengthen the pot's PCB pads!