If you're fully constipated then you won't be able to poop at all so in that case no you can't be fully constipated and still poop.
However there are some cases of people being partially constipated and being able to poop some but not be able to poop all the poop out like you should be able too.
Constipation in medical terms means having fewer than three bowel movements a week so well yes you could be constipated and still be able to poop some.
If you haven't had a bowel movement within a few weeks then you're likely constipated and if so you might want to see a doctor just in case you might have an obstruction in your bowels.
You could also try eating apples and other fiber based foods or drink some prune juice or apple juice which is also a good way to relive constipation.