Not yet, but as soon as the new role of the virtual machine becomes available, you can configure your own virtual server to support the classic ASP. There is no time indicated by AFAIK, but "soon" has been mentioned.
These servers will run on Azure hardware, but they will not run Azure Guest OS 1.x, so you cannot easily use Azure features such as Storage or AppFabric ... then you may not want the classic ASP environment :-)
EDIT: at the time of the request, my answer was correct (there was no full IIS), but a lot has changed, so the answer in 2012 will definitely be yes, as described below.
tijmenvdk
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