Hello

my two cents:

if you have interleaved slices AND if you are doing spatial smoothing
(with smoothing kernel bigger than between slice distance), then you
are also doing temporal smoothing with a simple "moving average"
filter (a very mild low pass filter) between current slice and
neighbouring slices half a TR away. Slice timing correction would do
the same kind of "moving average" but adjusting the weights based on
better interpolations (e.g. with sinc interpolation), so it is more
precise. Check this article
http://www.sciencedirect.com/science/art...

When it comes to functional connectivity (FC), if you are not doing it
at single voxel level with un-smoothed data, then most likely you have
some regions of interest that span across multiple voxels. Taking the
1st principal component will further temporally smooth the data (with
the same MA low pass filter). Furthermore, in FC they often band pass
the signal (0.01-0.08Hz) which means even more temporal smoothing ->
less effect on whether you time-slice-corrected or not.
Someone should do some tests on the effects of slice timing correction
and FC and write an article about it :)

best
Enrico