Yes, I have also experienced this. for me it will also have the beginner pop-ups from the champ select overlay over the main screen, since i haven't turned them off (the ones that say the banning phase is currently underway etc.) . and the champ select music will play, and i can hear the bans or i will fail to ban. I can enter shop during this period, and have successfully purchased runes during this period. i can also try to join queue again but it will say "you are assigned to an existing game"
The best way i've found to end up in the champ select screen is to join queue over and over no matter how many times it says "you are assigned to an existing game". when i do this, i find it is more likely and my best hope for ending up in champ select.
I find it especially difficult to deal with in an aram since i can't set up my runes or masteries and i won't know who im playing and i have a shorter time be able to rejoin champ select, and since it has alrdy chosen me a champion. there is (almost) no chance of a dodge.
It will sometimes dodge me, sometimes not. When i was duo'd with my friend, it didn't dodge me and he played a 4v5 while we were on skype. I don't recall if this was a summoners rift(draft) game or an aram. but i'm pretty sure it was a summoners rift(draft) game, since i distinctly remember him expecting it to dodge us.