There are two distinct aspects to prewhitening that need to be distinguished here.

1. Prewhitening the model equations to convert the correlated "noise" (part of signal excluded from the model) into white (uncorrelated) noise, so that least squares estimation of the regression parameters is efficient and statistics about those parameters are accurate.
2. Prewhitening the residuals, which are the data minus the fitted model, so that they are uncorrelated in time.

Mathematically, these operations are closely related, but for the practical purposes of FMRI analyses they are distinct.

The first one is for the purpose of producing the most accurate possible estimate of the regression parameters, the deterministic part of the model. In the context of rs-FMRI data, this deterministic model is itself of little interest, but is rather to be subtracted from the data to get the residuals -- which are the "signal" of interest now -- to be correlated across space, rather than time.

For the most part, people have generally done inter-regional correlations using the direct residuals, without prewhitening them -- that is, they use "-Rerrts" instead of "-Rwherr" in 3dREMLfit. There is no super-strong principle behind this, but it makes sense for a couple reasons:

1. Prewhitening a time series involves mixing values up across time points. In the case of 3dREMLfit, where the prewhitening amount varies among voxels, the amount of temporal mixing will vary between pairs of prewhitened voxel time series being correlated. It is difficult to wrap one's mind around the statistical and/or causal implications of this effect. [NOTE: this effect would be absent if the same amount of prewhitening was applied to all voxels, as in some other software packages whose names will not pass my lips.]
2. Temporal autocorrelation in the voxel time series basically downweights the higher frequencies of oscillation in the data, and prewhitening will boost those higher frequencies up in magnitude. Do you want to do that? Not so clear to me.

For the above reasons, it makes sense to me to use 3dREMLfit -Rerrts to "regress out" the deterministic model (baseline, baseline drift, motion effects, ...) and use the "plain" residuals for further rs-FMRI analyses. However, if one were to use 3dDeconvolve -errts instead, I doubt that the differences would be significant in the big picture of trying to understand the brain.