I have the same performance problem with Azure Web Sites, even in Reserved mode with a 2 cores engine.
Having deployed from VS2012 a site with a dozen of additionnal traditionnal modules, this site running ok on a dedicated Azure VM with the same configuration.
The site is using SQL Azure.
The site is using Localization and I installed 8 languages.
On Azure Web Site I have even adapted the config/HostComponent.config, with no apparent change: I am unable to switch to Admin Console, receiving a 502 error without any data in the DB after minutes of waiting.
The log file contains nothing, on the beginning I was thinking that deleting cache.dat and the various dependencies could recreate a valid environment but no success: everything is recreated but I still get the 502.
I just noted from time to time some connection problem with SQL Azure, may be the demo version? I have a Web Version with 1G and 98% free space...
It is clear that Orchard is not for Azure Website in demo mode, even using Reserved mode with large memory.
....I will open an issue for this.