For what it's worth, I've always extracted both the first eigenvariate and the mean time series and ran a correlation on them. I've never seen that correlation dip below 0.9 and most of the time it's > 0.95. While I've never formally tested an analysis (ppi) with mean vs. eigenvariate, I'd be willing to put money that, with the mean and eigenvariate being so highly correlated with one another, that the results of the analyses would be near identical.
But your mileage may vary, in our studies we concat across runs and have nuisance variables to correct for this so maybe it's in the way you adjust your timeseries. If the timeseries is clean enough then the first eigenvariate should be nearly the same as the mean, or so I would expect.