As far as min/max is concerned, it depends on which of the manuals you look at. In the Speer book, they list all their same caliber/weigh bullets with a single min/max load for each powder. This makes sense because with the same caliber and weight, you should have the same pressure and muzzle velocity.
What will be very different is down range performance. This is of course a product of the bullet ballistic coefficient. Again referencing the Speer manual, they list 5 different bullets in the 30-06 180gr catagory. All of them have the same min/max for 4064. The BC however ranges from .312 to .545, so very different down range performance.
If you subscribe to the theory that the timing of the bullet leaving the barrel and the harmonics of the barrel are what gives you accuracy or lack of it, same weight bullet, same speed equals same (similar) accuracy. In theory, based on my limited understanding, if all other factors are the same, and you have a powder weight that is accurate with a particular bullet weight, it should be accurate with different bullets of the same weight.
What will change is the POI though. Again, this is going to be based on BC and such, so if that changes, POI changes. Another thing that is subtle, but can have a great impact is the bullet jump (seating depth). Different types of bullets, even of the same length, will have the ogive at different lenths also. This will effect pressure and speed. So, this will also have to be the same for the different bullets to maintain the same accuracy.
Short answer, IMHO, is that if you have a charge that works with one bullet and is accurate, it should also be accurate with a different bullet of the same weight if all the othr factors remain the same.
Give it a try and let us know how it turns out. I'm curious to know if my thinking on that is right...