OK, let me try if I can get this straight in pure mathematical sense.

Yes, if you run 3dDeconvolve with -polort 0, the baseline (just a constant) would be estimated with those timepoints unspecified by all the regressors.

If you run 3dDeconvolve with -polort 0 and if your stimulus files are indexed with 0's and 1's and if all the stimulus files add up to 1 (i.e., the subject was performing various tasks all the time), then 3dDeconvolve would sputter with the following error message:

3dDeconvolve Error: Improper X matrix (cannot invert X'X)

The reason for this is that the first column of your design matrix X, which is all 1's, would be linear combination of those stimulus vectors. This would lead to an non-invertible X'X.

However, if you run waver with these same stimulus files, and then run 3dDeconvolve with the output as regressors, you would have no problem generating some results, and you would get the constant (-polort 0) estimated at each voxel. Well, this happens because running waver changed the picture of the linear dependence: the two regressors are no long linear dependent.

From modeling point of view, even if you could estimate the constant by setting -polort 0 in 3dDeconvolve, you would fail on catching the trend of the baseline, leading to a less accurate activation map.

Gang