How would one make a TCP connection from an Azure PaaS hosted Web Sites to a Worker Role? That\'s deployed in one virtual network. Can this be done without opening an Input Endp
You cannot add Azure Web Sites deployments to a VNet because there's no dedicated outbound IP address for Web Sites. This will also preclude you from setting up Access Control Lists (ACL's) on the worker role's input endpoints.
For Web Sites -> Worker Role (cloud service) security, you'd need to rely on something app-specific (maybe an SSL cert or something else).
By the way: regarding "a lot of work to do" for restricting access: Not sure exactly what you tried (or if you tried it), but it's trivial through the portal (just enter a subnet mask and... done), and very easy through command-line as well.
There are now two ways to connect to resources in your Azure VNET from your Azure Website. You can find details written up in several blogs.
The Hybrid Connections capability involves you downloading a relay agent that can access both Azure and your desired endpoint. This works for access to resources in your VNET or in any other network for that matter. You can install the agents on premise to enable TCP access to resources there. Each Hybrid Connection endpoint you define can only provide access to a single host:port. You can have 5 endpoints for free and if you need more you can pay to get them.
The VNET Integration capability allows you to access resource in your VNET. Under the cover it is using point to site technology to do this so your VNET needs a dynamic routing gateway and you need point to site to be enabled. If you also use site to site VPN to connect your on premise network to your VNET you can then access on premise resources.
None of these methods provide private access to your website. They only are intended to enable your website to access resource in other networks. Both features are also currently in preview and are being improved upon.
If you would like details on either there are a number of blogs and documents online. For an example you can refer to this one: using vnet or hybrid connections with Azure websites