Gonzo, I think you have the wrong idea of 'departing'. When an aircraft departs from an intersection, it means he has lined up there, and starts the Take-Off roll from that intersection. The Rotate and Take-Off point will be towards the far end of the runway...
Pilots of lighter aircraft often ask for departure from the most convenient intersection, if their aircraft does not need the full length of runway.
Multiple Line-ups on the Same Runway - SKYbrary Aviation Safety
Given similar types of aircraft, the second aircraft will always be flying under the previous aircraft's wake Turbulance. So you should never cross that turbulence, unless you deliberately try to out-climb the leading aircraft.
I, too, will make it clear to any and all users of this board that in my view Gonzo knows what he is talking about. A simple review of his posts should very quickly highlight that he not only knows the rules but also understands their practical application to different situations.
There is a difference between knowing and blindly applying a rule, and understanding a particular topic sufficiently to discuss the merits of any particular element. This discussion started with a question about a rule - for which there is a fairly straightforward answer. But with this topic, more than many others perhaps, just applying the rules will not guarantee to keep everyone safe. The rules will provide a basic level of safety for many, maybe most, situations, but they will not ensure that a pilot/aircraft will never encounter the wake turbulence created by another aircraft - they will, hopefully and with a fair wind (see what I did there?), prevent a severe encounter. This is why it is important to understand how wake turbulence is generated and how it disperses and dissipates in different weather conditions.
There is a very good UK
AIC on the topic which discusses separations and, of particular interest, the development of time based separations which are intended to take account of the more rapid dissipation of turbulent vortices in certain wind conditions, and where/how the hazards are created. Should be essential bedtime reading!