Probably not uniformly double on all aspects. Single threaded won't.

Workloads that high stress the die interconnect probably won't if go past two dies. GPU performance has gone up perfectly linear across all workloads from. M1-> Pro -> Max so likely won't for anything in a Mac Pro ( Ultra and "better than Ultra")
Can look at the Studio's marketing page on Apple site in the graphics performance benchmarks they cover.
https://www.apple.com/mac-studio/
GPU
Final Cut Pro : 5/3.5. -> 1.42
Compressor. : 12.6/7.5 -> 1.68
Affinty Photo: 4.5/3.4 -> 1.32
Borris. : 2.6/2.0 -> 1.3
Maxon : 2.6/2.2 -> 1.18
Blackmagic : 2.3 / 1.3 -> 1.77
CPU
vectorworks : 1.6 / 1.3 -> 1.23
affinity photo. 1.5/ 1.4 -> 1.07
NASA TetrUS 5.3/2.7. -> 1.96. ( a codebase from decades long supercomputer optimized legacy )
The Ultra doesn't uniformly double the Max. More does likely lead to more partial flattening hiccups for some codebases.
Folks say that and it tends not to happen. Many folks are on a depreciation schedule or a fixed budget or both. Tend to let go of machines mostly on a schedule so no "panic" dumping of those systems. Others are on "buy when need it" schedule. Vast majority of those who bought a MP in 2021 isn't going to dump it fast (unless it is a problem and would dump it anyway).
Macs tend to hold their value over time because the demand/supply for used system is pretty balances most of the time. Mac Pro tend at a relatively slow rate to the rest of Mac systems that retailers (and Apple) don't have massive warehouses full of 'toxic inventory' to dump at product transitions. Discounts? yes, but panic selling? no.