Possibly, but the air flow will be in the direction of least resistance.....is that the base of the screen or engine bay in this case? I've never tested it, so assume they would have. My bet is the base of the screen is lower pressure than the engine bay.Amen to that.
I think they are using those holes to push fresh air into the engine bay as that is what would happen if you closed off the cabin
Usually the screen base is easily higher pressure than the cabin, but I reckon the engine bay would be the reverse especially at speed.