for a 2 PM arrival, I think you should be fine. This last time at Bay Lake, we landed around 6, got to Bay Lake around 7 or so, and I am pretty sure our bags for there around 9:30. That said, I had a less than stellar experience in March at Pop Century. I landed a little before 5, and was at Pop Century at about 6:15. So I called at 9:30 wondering about my bag and was told it was there and would be delivered "soon". So I expected the next 30-45 minutes to see it. 11 PM rolled around and I called again and was told they were just getting ready to deliver to my building. I heard him turn to the other cast member and tell him to deliver to my room first since I had called twice already. It showed up at 11:30. I was not too happy, but moved on quickly from that.
I am going again March and my flight lands after 7 (as of now, I expect it will move slightly). I am thinking I may pick up the bag. I am staying at Pop again and after last time, I am not as confident in the time it will take to get my bag. I still have a bit of time to decide and see if my flight time moves at all.