Not always.
I believe "Oh" can represent either "おお" or "おう" since it is more of a phonetic representation, versus a romanization based on the written characters.
For example, names like the ones below could all be written with the "Oh" even though they are "おお"
(I actually know people with these names who write them with "Oh" on their 名刺)
大柳 - おおやぎ
大野 - おおの
大家 - おおや
