confound regression: could it be done outside the cross-validation loop?

[jcrdubois]

we should think whether the confound regression could simply be done on all subjects without introducing any meaningful leakage of information. What we do is very safe, but perhaps overkill and unnecessary

[paola-g]

We could and I think it's a very common approach in literature, even though some advocate a cross-validated approach is the best way to reduce bias.
Do you think it impacts substantially the computational demands?