Risk prediction in Cox regression using counting process style of input

I fitted a Cox model with age as the underlying timeline (entry=baseline age, exit=age at event/censoring) to estimate hazards ratios for an ordinal exposure on all-cause mortality. The counting process style of input, which here fits a non-parametric function of age was ideal due to difficulties in fitting an appropriate functional form of age (using time in study as the timescale).

Now, I am interested in determining the C-index for the Cox model with and without accounting for exposure status (I am aware of the various other metrics to quantify added predictive value of new measurements). My question is this:

Is it meaningful to estimate Harrel’s C-index from the Cox model using age as the underlying timescale (http://bioinformaticstools.mayo.edu/research/survcstd/)? Or is a Cox model with follow-up equal to days/years in study since baseline ascertainment of exposure status, a more appropriate model for the evaluation of of t-year predicted risks (obviously the latter model would then need to be adjusted for age at baseline)?

My thoughts: In this particular example, exposure is not a stochastic time-varying covariable (=exposure changes as a function of increasing age). In my opinion (non-statistician), this means that exposure status in the entry,exit Cox model should have been determined at all individual failure time for hazard ratios to correspond to absolute probabilities (=exposure status at entry could be completely different different from exposure status at the age of event/censoring)? As I see it, the pairs being compared in the entry,exit Cox model are not necessarily the appropriate/correct pairs.

Any ideas/thoughts would be greatly appreciated.