The short answer is no.
The long answer is that I think men and women are different and because of that I would say yes.
Don't get me wrong, I tend to be the last person who remembers that it is possible for volunteers to get robbed or worse on the streets of the colonial zone at night. I tend to be the person who says she is going to walk home alone and Gracias a Dios I have friends who stop me and remind me that danger does exist. I'm stubborn enough to say a woman should be able to be alone in every situation when a man would be alone, but I'm smart enough to know that this is not the case.
I don't think that being a young woman in the Dominican Republic is any more dangerous than being a woman in the United States. I would want to walk around alone at night in the U.S., but I wouldn't always feel safe and I want to walk around alone at night here, but I also know that this isn't always safe.
This is mostly related to women being more likely to be assaulted or robbed because they appear weaker or as an easier target.
One thing I need to do is I need to change my mindset. I suffer from the typical "It can't happen to me" mindset. I've said, "Why would anyone want to assault me?" more times than I care to admit. I think that going through scenarios in my head as I walk is sufficient preparation for when someone actually pulls up on a motorcycle with a gun and demands my purse. The thing that actually scares me is that I know I am one of those people who does NOT want to give up my things. I don't want my passport to get lost, I don't want my actual bag taken, and I don't want some creeper having a piece of me. Any time I run the scenario in my head I tell the thief to "shove it" and I hit him in the face. In my altered reality of this situation he is so shocked by my denial that I have a window to escape. In reality, I'm not so sure this will work.
Another thing to note is that I did get a site change and when I tell people about my site I always say, "My site wasn't necessarily bad, but it would have been better if I were a guy." I also say it's a fine project to send another volunteer to finish, it would just have to be a guy. It was awful being in my first site for those 8 months. I stress called my best Peace Corps friends and staff constantly. I was anxious and upset for 6 straight months. I also think all of those things wouldn't have happened if I were male. The uncomfortable actions that were taking place either wouldn't have happened, or wouldn't come across as inappropriate if I were a man.
In the end, being a woman in a foreign country is different from being a man, but at the same time, being a man in a foreign country is different from being a woman. This is to say, it's all the same. We just face different issues.