The problem is that Apple's in-store Personal Pickup tool is generally not a reliable indicator of a specific launch date or Apple event. The in-store pickup date for 12.9-inch iPad Pro models is a rolling target, as evidenced by the April 5 date now shown just one day later. Tomorrow, it will likely show April 6.
The date shown is most likely just a rough approximation of the 12.9-inch iPad Pro's current 2-3 week shipping estimate, plus a few extra days to reach the store. On February 9, for example, we reported that most 12.9-inch iPad Pro models were available for in-store pickup on March 3 at the time.
Apple could still hold an event on April 4, especially considering many of its past events have been on a Tuesday, but it would be purely coincidental.
Personal Pickup does confirm the 12.9-inch iPad Pro remains in tight supply, which can sometimes foreshadow an upcoming product launch. In January, however, Apple said it had an issue with one of its iPad suppliers that was not expected to be fully resolved this quarter, which could reasonably explain the shortage.
Apple is expected to launch at least a trio of new iPad Pro models in the near future, though, so an event might be announced soon enough. Japanese website Mac Otakara said Apple is planning a March event where it will unveil those new iPads alongside a 128GB iPhone SE, red iPhone 7, and new Apple Watch bands.
An all-new 10.5-inch iPad Pro with an edge-to-edge display and updates to the current 9.7-inch and 12.9-inch models are rumored. A new 7.9-inch model is a wildcard, as reports are conflicting about whether the iPad mini 4 will live on or be replaced by a lower-cost 9.7-inch model as predicted by KGI Securities analyst Ming-Chi Kuo.