This is not clear in the available research and it's a good idea to speak with your doctor
before traveling. While traveling abroad can be quite enjoyable, there are certain stresses that can come with it as well. Unfortunately, as mentioned previously, there is not a significant amount of research suggesting whether or not yogurt, specifically with pro-biotics, can help to avoid gastro-intestinal problems while traveling abroad. In general, it is thought that the bacteria in yogurt represent "good bacteria" that can help to colonize the GI tract and prevent "bad bacteria" from taking root. Unfortunately, many of the germs and bugs that can get you while traveling abroad are unlikely to be affected by the bacterial flora that may be living in your intestines. Some of these include parasites, which function on a much larger scale. So, while eating yogurt may help your GI tract to be healthy, it is not clear that it will prevent problems for most people while traveling abroad.
Your idea of maintaining good health while traveling, however, is right on. Speaking with your doctor before traveling can help to identify anything that you CAN do before you go, such as get additional immunizations or pack extra supplies and even antibiotics in some cases. Please speak to your doctor.