Yes. Having a day of being sick was the thing that made me know I was expecting my daughter, even before the "usual indication" women get.
All pregnancies and all women are different (as I know you must already know), but just so you don't get too discouraged with being sick this soon, being sick early with my daughter wasn't a sign of things to come later in the pregnancy. After that one episode, a pretty minor one that came later, and a long stretch of not really being sick but also not wanting to eat either; I didn't spend much time being sick.
Then, too, it could be a 24-hour bug. Also, there's the chance it isn't "technically" morning sickness but, instead, could be that you ate/drank something that otherwise wouldn't have bothered you but did, now that you have a new pregnancy. There's kind of a subtle difference between morning sickness that has little to do with what you've eaten or not eaten, and having a bout of vomiting as a result of having eaten something that your now more sensitive, system could handle.
In any case, morning sickness pretty much does its own thing, has no "rules", and can be almost non-existent, only mild or occasional, or very severe. (With my son, the only way "morning sickness" showed up for me was that I would vomit each day at 3:00 p.m., like clockwork, right up until 3 weeks before he was born. I can only assume it may have been related to getting up the same time each day for work and eating the same stuff for breaks and lunch every day. It did show up faithfully on weekends too, though. Go figure.