Short answer: Not usually. If you're using a "normal" sized toy or body part of about 7 inches or less and your rectum is empty then no, usually anal play will not cause you to poop. Note that you might feel as though you need to go. This is especially common in people new to anal play, as your body usually interprets something in the rectum as meaning that you need to poop, but usually nothing will come out. This reflex will often be reduced as you have more experience with anal play.
If you're playing around with long toys (over 7"), and you don't do anything to "clean out", then it's possible that anal play could lead to pooping. Poop is usually "stored" in the sigmoid colon right above the rectum, and if a toy enters the sigmoid while there's other stuff in it it might cause it to come out.