is it possible to make ethanol from ethane through a chlorination / hydrolysis two-step procedure?
Yes, it is possible.

Although ,commercially(and ironically!) alkyl halides are produced from the corresponding alcohols.
The main reason why this is so because free-radical chlorination requires high temperatures and catalysts to promote the reaction.

Theoretically, the first reaction will give good yields(and not a mixture unlike most free radical halogenations because of the simple reactant involved)

Edit:As pointed out by bon, I forgot to take into account that because its a free radical reaction, the number of possible products is a lot.So no, the first reaction will not give you good yields.