Yes, if you say "on the other hand" without a preceding "on the one hand", that meaning is implied.
Indeed, people often use the idiom this way in conversation, as opposed to writing, when at the time they make the first statement, they have not considered that there is a drawback or an alternative. Like two friends might be chatting and one says, "Time for lunch, let's go to McBobs. [pause] On the other hand, we go to McBobs all the time. Let's go somewhere else today." This would be less applicable to writing, where you would likely edit the sentence to add "on the one hand" before the first option.
And I am suddenly reminded of a review of a book by Peter Shickele: "On the one hand, Peter Shickele is very funny. On the other hand he wears a ring."