If battery is nearly dead, and you jump or bump start the car, then running it, particularly on a long journey will boost the battery charge (unless of course there's something gone wrong with the system in the first place)
Me, years of experience, with both Alternator and Dynamo (yes, really!) equipped cars.
... how else would you, for example, flatten your battery accidentally in, say, Scotland, get the car started by the RAC, then drive home to London without a) booking yourself into a hotel b) getting a battery charger from somewhere and putting the thing on charge overnight c) re-fit it to get home the next day?
Typical charging voltage from an alternator is c14.5 volts - which if the battery is discharged (down to say 10 volts, I think it is) then there's ample to give the battery a good charge-up and get you home - even at night.