Close, yes.
You can freely drop down in the ratios you prescribed. However, if you want to split up one of those that you just split up further, you can only do it for two of the lower priority.
So, you start up With 1 Battle point? How many Skirmish can I get?
Answer: 3. But it's not a great swap.
I could break down to 2 Raid. Can I then break down each of those Raid to 2 Skirmish?
Answer: No. After the initial breakdown, you can only break down 1 point of the remainders. So I can break down the 2 Raid, yes --- to 2 Skirmish (from 1 Raid) and 1 Raid (which I can no longer break down.)
This is much better than those 3 Skirmish, now, aren't they? Because of this, Armageddon puts a high priority on having competent ships at all levels below War. Most races have holes in here somewhere, which makes it -- I guess interesting: Narn Raid isn't very good, Minbari Skirmish stinks, Dilgar Battle is pretty substandard, Crusade Skirmish is a wasteland, Centauri Skirmish is a mixed bag (hope you like the Maximus), ISA needs allies at Skirmish level and doesn't have enough of them, Old Ones have large warts at Raid and below. Third Age is a major exception, and the League as a whole is fine. Drakh have good choices at most levels as well.
Can I break down those Skirmish points?
Answer: Only one of them. Again, after the initial breakdown, I can only break down 1 Point from these lower levels.
So after all this breaking down, I can get from 1 Battle point to 1 Raid, 1 Skirmish, and 2 Patrol.
If I'm in a 6 Battle fight, can I do this with each battle point?
Absolutely.
Hope this example helps!