Do I have to re-intonate the guitar when I change the tuning?
Only changing tuning, probably not. Changing strings to cope with different tuning, probably yes. I think the intonation is far more dependent on the guage of the string than how loose or tight it is. However, if the tension change is notable, looser strings mean more rattle propensity, so higher saddle, maybe needing intonation changes. If the tension is higher, and the action is high, even with no change, you may find yourself playing sharp due to the increased tension of fretting. Just another by-product.