My inclination is to say that you don't want to use 3dREMLfit for this purpose. The nonwhite noise for task FMRI studies is now your signal so why whiten it? However, there are multiple sources for noise in resting state signals, such as respiration and heart rate. To the extent that you do not model them properly and regress them out, they would affect the estimate for the degrees of freedom.
As Bob said, this merits closer consideration.

Are you making statements about individual subject connectivity maps or are you using taking the connectivity maps to group analysis for the final results ?
If the final result is group analysis maps, then using 3dREMLfit or 3dDeconvolve should make little difference.

cheers,
ziad