Does the full ritual bath suffice in place of the ablution?

If a person takes a full ritual bath on Friday or to cool off, and intends the ablution, does he have the ablution, even though he washed his limbs in order?
If he washed them in order, it becomes an ablution. However, if he washed his entire body without order, then if it was for major ritual impurity, or for menstruation in a woman, it suffices for the ablution. But if it was to cool off or for Friday, it does not suffice; because this is for something other than a state of ritual impurity.