Sure, just set the mixes for the constraint to zero, then back to what you want them. You can do it in animate mode to ensure you don't mess up your setup pose. Plus then you don't need to set them back to the old values, just delete the keys or temporary animation. If you turn off auto key, you don't even need to do that.
We used to have a visibility dot for constraints, to quickly turn them on/off. This was lost as things got more complex and we found the visibility dot was not really needed. Setting the mixes is simpler and achieves the same goals.
