It is likely still possible, but would probably require a lot more complication and work than it is worth to accomplish. You would likely need to create your own custom event handler code to accomplish this. And depending on your expectations of how/when it should work, you may need to create your own add-in to accomplish it. I've created some custom event handlers before, but not one for this specific event. I'm not even sure there is any event defined or exposed to the API for specifically just when you first enter into the Edit mode of a sketch. I know there are ones for when you create a new sketch, when you delete one, and when a sketch 'changes' (complex meaning - when geometry actually changes as a result of the 'change'). These can be tricky to create and set up correctly, and you also have to have a plan for removing/destroying any custom event triggers you create, usually due to some other event happening.
Here is a link to one of my contribution posts that can get you started down that road, if you choose to do so. It's not for that specific event, but there's a lot of good information there for dealing with other types of custom event handlers too. The closest thing I can find to what you might need to work with is the SketchEvents object, and its 'OnSketchChange' event. I dabbled with it a little bit, but don't have any complete working examples to post for you.
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Wesley Crihfield

(Not an Autodesk Employee)