If a given bike has a head tube 1.5cm shorter than another, but the one with shorter head tube has a 1.5cm lower BB drop, given all other things held constant, these should be the same for positioning?

There are too many variables that you haven't mentioned.
If the seat tube angle, head tube angle, fork length, fork rake, and top tube length are same (and both manufacturers use the same method of measuring)

For positioning what?

Assuming that you meant the rider then I'd have to say yeah, The shorter headtube would hold the bars 1.5cm lower but the lower BB would also require the rider to sit 1.5cm lower. But that's a big variation on the BB height unless you're comparing a road to a cyclocross frame.

Why don't you model it and find out?

https://www.os2.dhs.org/~john/Bicycle...try/index.html

The simple answer is yes, you could get the same vertical position, assuming both bikes use the same type of headset and fork lengths are similar. Road bike forks don't vary greatly in length, unless you're making an apples to oranges comparison of a racing bike to hybrid or cross bike.

The total fit comparison requires more info, like the TT length and the STA to define the reach.

Sweet!

Open source ethos FTW : D