Actually, the rule specifies that the insufficient losing chances in sudden death option can be used with a delay/increment capable clock, if the delay or increment has not been properly set.
However, the default version of rule 14H is that no claims of insufficient losing chances will be permitted at all, no matter what clock is being used. I think this is the clearly superior rule for TDs to employ. The rulebook takes up over a page and a half to explain all the details of ruling on an insufficient losing chances claim. Why invite such complications? Digital clocks with delay/increment capability have been considered the most standard equipment for over 30 years now. Anyone still using an old analog clock should be prepared to pay the price for using obsolete equipment.
As far as I know, CCA does not have any (non-blitz) tournaments without delay. The CCA rules do have a provision for insufficient losing chance claims. The wording of their rule 15 refers to situations in SD controls “…where delay or increment is not used…”, which seems to hedge the bets: it will primarily apply to cases with analog clocks or digital clocks which are either not delay/increment capable or which do have the capability but were improperly set. However, the possibility of an event where neither delay or increment is mandated is left open, even if it is no longer used.
As Micah notes, the prescribed procedure under US Chess rules if delay or increment has not been set is to add a delay/increment clock (rule 16P1). However, CCA rule 17 has a slightly different procedure, which I think is superior: The TD is not required to add a delay/increment clock; that is just one option. This is so that a player who has used an analog clock or (perhaps deliberately) not set delay/increment and gets in time trouble cannot, in effect, “claim” a digital clock.