No, it usually waits at the NVC until Montreal gives the green light for the next batch of interview slots, and then the NVC will schedule/send it for you.
Now, as far as I know, or as far as I am predicting, they typically cut off the DQ date somewhere in the third week of the month. As I have observed the trend here, you are looking for roughly 10 ish weeks from DQ to get IL. But it's just my observation, and there is no data to back it up.
For example, my wife DQed on March 6, 2024, and the last time I checked consular operation pages last month after they updated on April 19th, they tried to schedule all the people who DQed in February 2024. Judging by posts on Reddit r/ NationalVisaCenter, people who DQed before 2/14/24 or a similar DQ date got IL on 4/17/24 or 4/18/24. So, with this limited data, I think my batch (Second half of Feb 2024 to mid-March DQ date) should receive IL in the coming dates if my prediction is correct.
Fingers crossed, and let's hope that we all get IL in a timely manner.