I really don't see any advantage in what Mclaren are doing. Teams would want as much track time as possible with their new challengers. The data collected will also be invaluable even if it means spending a bit more time in the garage.
Mclaren may also find themselves in the situation where the Pirelli's suit their old car and not so much the new one. In that case it would have been better to test the new car from the get-go in order to iron out potential issues.
As for those who think that Mclaren are hiding something I would be willing to bet that if any team has a golden bullet it will only make it's way on to the car at a later test. Hell, I've read reports that say Ferrari have recovered much of the lost downforce related to the ban on the DDD.
The thing is they aren't running an "old car", its an interim car, so its not a 2010 car and it isn't the 2011 car that will start in Bahrain either.
Whenever you test something (could be anything, not necessarily a car or even motorsport related) and you have a bunch of variables you only really want to change one thing at a time, because if you change two things and see an improvement you don't know which change caused the improvement, it could be that the two things fought each other and you'd see a bigger improvement with just one of the changes, or that one had no effect or they both worked together..
So as others have said it could be that using a 2010 chassis they can get a baseline on where the tyres car, compared to the bridgestones. That could be useful to tell them how the chassis setup needs to differ for the pirellis.
Personally, I think they've already done this at the tail end of last year and will now run 2011 aero parts on a 2010 chassis, again using knowledge/data of the 2010 chassis as a baseline to test the 2011 aero. Lets not forget that the last two years (at least) the McLaren has been a bit of a turkey at the beginning of the season - they aren't stupid and must of had good wind tunnel figures on the aero that was devised, yet when mated with the chassis the two didn't work together very well, and I think they struggled to understand how or where the problems were - at that point they had to ask do we change aero or chassis ? or both ? if we make an aero change how will it affect the chassis and any potential changes we make there ?
They know the characteristics of the 2010 chassis now, so they can quantify the 2011 aero more accurately and not go down "blind alleys" with changes that are wrong, particularly to the chassis.
When the second test comes around they'll have some aero data to work on, so will be able to quantify the chassis performance with more accuracy.
I think its all a move to improve efficiency in the development cycle.