Yes. I eat oil-free and low fat/fat-free whenever possible. You can also look at this post for Vegan Anywhere.
First I look at the menu for dishes that could fit the bill (which means skipping past anything that's fried). I specifically look for things that can be steamed or are not cooked (i.e. fresh spring rolls in a Thai restaurant or a salad). I'll also inquire whether my meal can be made without oil. Most often it can, if not, I'll ask if there is another dish that could.
If I end up with a salad (or that's just what I want) I skip the dressing, and ask for salsa (if they have it) or vinegar. If I'm dining solo, I'll also ask them to hold the nuts and avocado -- or anything that might be fried.
For example, I recently ordered a salad that normally came with fried tortilla crisps, and I had them hold that, but if I'm out with friends I'll just pick off the nuts or avocado because someone at the table always wants my discard. And if something looks oily, I will send it back. I'm never embarrassed about that.
Likewise if I eat something and I can tell it's really oily, I stop eating it and order something else. That said, now that I'm at a healthy weight (and I have maintained it for a while) I do splurge on occasion and, say, get a slice of vegan pizza with friends. Or I'll get a vegan cookie, or a slice of vegan pie which will I'm sure has some kind of fat or oil in it. I try to share desserts, and if I can't share, I have a few bites to be satisfied, then discard the rest.