This really has little to do with Azure. You can of course make external connections from inside your virtual network to services that are not running in Azure, Azure services all have internet connectivity. You will need to make sure that any NSG rules, Firewalls etc. allow this traffic but you can do that.
Support for multiple users is down to the service you are connecting to, it has nothing to do with Azure.
Connectivity speed is again going to be down to the connectivity of your application to Azure. Bandwidth up to the end of the Azure network is very fast, but once you leave that it is going to be down to what connectivity your application has.