Although watermelon doesn't contain a lot of fiber the watermelon does have some fiber which can make you poop.
Watermelon is also 92% water which also gets bowel movements going and makes you poop more often.
So yes if you eat enough watermelon you can be ready to poop soon after or even have diarrhea if you consume too much watermelon in too short of time.
Watermelon can also make you pee more too since it's 92% water and when you intake more water you have to also pee more often.
Watermelon is great for your health so eat as much as you can but just be ready to poop or pee soon after if you eat too much of it.