Q: Can I run 32-bit applications in Windows Azure Infrastructure as a Service?
A: Windows Azure Infrastructure as a Service (IaaS) supports only 64-bit OSs but remember 64-bit OSs can run 32-bit applications through their Windows on Windows (WoW32) subsystem. This means most 32-bit applications will run fine on a 64-bit OS (remembering 32-bit drivers can't run on a 64-bit OS) and therefore should run OK in Azure IaaS.
It's important to remember, however,that just because it runs doesn't mean the application vendor supports running on Azure IaaS, so you should always check with the application vendor. To learn which Microsoft software is supported to run in Azure IaaS check this list.