Is this bulge in my ceiling due to a roof leak?
Based on the picture that was posted in a comment (then added to the original question). It looks like this was a poorly done patch.
At some point in the past, someone had to remove a portion of the ceiling drywall. Possibly to repair a leaking pipe, to repair a water leak from outside, or some other reason. When the person (a lazy contractor, or a previous home owner) went to replace the drywall on the ceiling, he either:

didn't have the correct thickness of drywall to match what was already on the ceiling so installed a thicker piece that he had on hand
didn't attach the correct thickness of drywall well enough, and one end has begun to sag

This just looks like a poor repair job, not a current leaking spot. However, it's possible that if there was a leak here before, that the spot (whether plumbing above, or something coming in from outside) is leaking again, and it bears keeping an eye on it.
Whether one would &quot;notice drops on an iPad&quot; seems to be quite irrelevant to the question. Look for additional signs of water damage - additional sagging, damp to the touch and/or discoloration.