...or it could be used to asses delay discounting function from procedures that use other measures of reward value, like proportion of choices of the larger later rewards?
In my opinion, yes: the hyperbolic function describes the relation between 'value' and delay. 'Value' may be measured as the size of an immediate reinforcer that equates to the delayed reinforcer (in behavioural terms, equal value means indifference in a choice situation). Alternatively, 'value can be eliminated from the equation by the laborious process of obtaining indifference delays to a larger reinforcer for a range of delays to a smaller reinforcer, and then plotting the indifference delay against the delay to the smaller reinforcer (described by Mazur, 1987, An adjusting procedure for studying delayed reinforcement.In: Commons M et al (eds) Quantitative analyses of behavior, vol V: the effect of delay and intervening events. Erlbaum; also Ho et al, 1999 Psychopharm146:362–372). The relation between %choice and delay is better described as a 'preference function'; its shape is not intrinsically related to the hyperbolic discount function (Valencia-Torres et al 2013, Eur J Behav Anal 14 313-239