The theoritical advantage in locktime on the falling blocks ( if it exists I just don't know ) would be negated by the negatives of the two piece stock design.
For very accurate rifles the best judge as to what works is to look at benchrest match results and see what is winning. Focus on two classes the all out unlimited where the only real restriction is wieght, and the Hunter Class which is a box stock factory rifle, no modifications of any sort allowed.
In the unlimited class custom bolt actions rule, names like Hall, Stoole, BAT and Farley are in the winners circle. Very rarely will you see a reworked Remington 700 or 40X action, although the current 1000 yd record is held by a Savage action. The factory actions are not even close to stock and have had extensive work on them. Bottom line none of these are falling block actions all bolt actions.
Moving to the Hunter Class there is one dominate force Remington, either a 700 or a 40x, with Savage starting to make interesting headroads. Right now big green wins about 80% of these matches with various rigs, the only real competition is coming from Savage lately and the last year or two the Savage rifles have really started to come on strong and won matches ( about the time the accu-triggers became available). Winchester is odd man out here, seldom do you see a Winchester in the winners circle. I think there are a couple of Winchester that could compete like the new FN sniper rifle but I think cost of the rifles is an issue, not capabilities of the rifle. Other rifles seen on occasion are Varmit Tikka's and Sako's, I don't ever remember seeing a Ruger being on a winners list. I am not saying the other manufacturers rifles can't compete and some do, I am just saying using anything besides a Remington right now you are definately fighting the odds, although I do believe that cost is a deciding factor, cheapest out of the box accurate rifles are Remington and Savage.
The Hunter class is what to me represents what can be expected when you buy a rifle, again I emphasis no modifactions are allowed on these rifles to compete.
I should note that both of the above are tough competitions. A straight hunting class rifle usually can't compete because the barrel profiles are too light and when shooting five round groups quickly the barrels heat up and start to string the last couple of rounds. Varmit rigs fair better because of the heavier barrrels and the Police versions of these rifles do very well.
I think you could work a falling block design to get .5 MOA but I think that would be the limit and would take some serious working on it to get there. I recall reading about some parts needing to be changed out which tension the barrel to the action, but this won't correct the two piece stock, which in the accuracy game is a whole set of factors that would need to be dealt with. Most really accurate rifles today are free floated and the barrel and stock don't come into contact. Time and money could probably correct this but my guess is it would require a lot of both to really get down into the numbers required to win. Just for reference the current record for a 5-5-100 ( five shots, 5 groups. at 100 yds ) is .1283", and no it wasn't done with a factory rifle.