Haha yes it does mean that, although dump/shit is a rather crude way of saying it. You would only use these two around friends/family who you were very comfortable with and weren't worried about offending. Poop is less offensive, though you would still use this only with friends and family. You might use 'poop' (American English) or 'poo' (UK) with your children. In the UK, you would might say "I haven't been to the bathroom/been able to go to the toilet in two days", referring to the act rather than the result. You could also say "I'm constipated. I haven't been to the toilet in two days". These would be the kind of things you might say to your doctor or when you want to be more polite.

It's been two days since I've taken a dump. or you can say I have not pooped in two days. both correct. not sure which one is more polite.