This is more of a request for seasoned 2nd edition players (which I am not) than a proposed variant.Don't do this. Assuming you don't tamper with any other rules, this would allow hunters to draw events 3 times in a row (assuming nothing was found by searching) without giving anything to Dracula, while being able to move at the same time. At night they could simply not draw events meaning that Dracula would rarely (or possibly never) get an event during the game.
What do you think about drawing Events from the top (and discarding Drac's ones) during the 3 day turns, while drawing Events from the bottom (and giving the vampire's ones to Drac) during the 3 night turns?
This may also be a slight problem in third edition, but at least in that hunters might find themselves forced to supply at night due to wanting to move during the day.
As 2nd edition is already considered by many to be hunter biased, any change that would shift the balance away from Dracula is to be avoided.