Am I more likely to get gastroenteritis during international travel?

Depends where. In countries with poor sanitation systems, bottled/purified water is the only way to go. Gastroenteritis is much more common in underdeveloped countries and in tropical areas. Check with local health authorities or the CDC for areas to which you'll be traveling for more detail.
Good Chance. In spite of wise precautions, the longer you travel, the higher your chances are for traveler's diarrhea. Naturally this fact depends on where you are traveling. Studies show at one month of travel your risk of gastroenteritis is greater than 50% and increases in risk for each week of travel beyond that. Learn how to stay safe and carry back up antibiotics, pepto-bismol, and imodium (loperamide).