Absolutely. I've had above-ground pools, and let me tell you, it is no small thing to drain the pool. First, it takes considerable time, and second, you're going to end up with a lot of water, even from a 3 1/2' pool -- it would definitely be an issue.
As to the idea that someone might have drained the pool and then buried the child beneath it, one needs to understand that the pool liner is very heavy and that the ground beneath the pool would have been prepared -- leveled and then sanded, usually with nearly a half ton or more of sand. The wall of most above-ground pools (if quality) is made of steel in one continuous piece which is bolted together at one point -- you can't simply "pick it up" and move it --the wall alone would easily weigh in the neighorhood of 200 pounds, without the liner attached. The operation would require a minimum of three people, more would actually be necessary if you didn't want to risk damaging the wall or the liner when you tried to move it to bury the body -- which would be essential if your plan was to place the pool back as though nothing had happened. I can't imagine that you could pull it off without leaving clear evidence that you had done something with the pool -- there would be sand from the "cove base" all around the reset pool, as well as damage to the lawn from the weight as you were moving things around. Most importantly, it would be nearly impossible to avoid damaging the pool in some way during the operation.
Now, people do (and I did more than once) drain the pools for cleaning, etc. -- but it's not something you do as a rule. Most of the time you just drain them down to about 1/3 depth and cover them for the off-season -- then condition and restart the water when the new season begins. Above-ground pools are simply not designed to be moved once they are installed.
The bottom line is that it would really be nearly impossible to do this without lots of help, and no small amount of luck. Could the whole family have done it together? Sure, but I think it's exceptionally unlikely.