not if you want to adjust runes, and especially as lastpick, if you lock in and then start on your runes, you get a very tight window for doing them.
Also, not all people are OTPs or have a clear idea what champ they want that game, some, like me, play almost any champ and take all previous picks into consideration when pondering what champ to pick, and if you last second switch, you might be to late for the log in.
I for my self would prefer spending another 1-2 extra min in champselect over either haveing a leaver or some panic-picked champ or someone with the wrong runes on my team.
The high impact that champselect and runes have on the game are in no relation to the short time we get for them...