No, not currently. The issue is that I wouldn’t want search results updating automatically as you are editing or issuing commands. For example your typing (or commands) could effect search results making the current item that you are working with disappear as you are working with it. TaskPaper is different then most search UI … because you are “live” editing everything, instead of going into a separate “edit” mode, and then committing changes. I think live editing together with live search doesn’t work well, or at least I don’t know how to make it work well.
I can imagine cases where maybe it does make sense to automatically refresh results … like maybe when you switch to a new tab you update the results. But even there it could create trouble. Like maybe you were previously adding some items to that view that don’t match the result… go back expecting to see them, and don’t.
For those reason I don’t expect live search to ever be a default. I think best for now is just View > Refresh Editor Search (Command-R)