Supposing one were to compile a native dll using IPP (Intel Performance Primitives), and deploy it to Azure using a managed wrapper, would the performance gains from IPP be realized?
I would not count on it. I know that AMD Opterons are used in at least some (if not all) of the Windows Azure physical machines. Some actual machines might be Intel based, but you have no control over choosing the CPU make.
EDIT: There seems to be a bit of confusion here about what I mean when I say "I would not count on it". Essentially this question boils down to, "Can I count on specific hardware optimizations performing at peak when I cannot control the hardware it runs on?". Putting the question like that it should be obvious the answer is no.
Note, this answer does not say that IPP will NOT work or advise you not to use IPP. It simply states you should not count on it working or even if it works, working at peak performance.
Even if I knew for certainty that IPP (or any optimization) worked in Windows Azure today, my answer is still the same: do not count on it. Microsoft is certainly not buying the same server SKUs it purchased 3 years ago when building the platform and the platform itself is likely to change over time. So, even if something worked great today, there really is no guarantee that it will continue to work the same way should hardware change yet again. At least no guarantee until they allow you to specify minimum hardware SKUs.