Yes, it's definitely possible to develop your channel using an Apache server on your local network. When you specify a url in your Roku code, the Roku doesn't care where the resource is located, whether it's on the local network, or a remote host. It's more a function of your network's router to route the requests to your local server. How you do it depends on your particular router.
In my case, my router has a "DNS Host Mapping" feature that allows me to associate an IP address on my local network with a domain name, so that any requests from a device on the local network (e.g. my Roku) for the specified domain name (e.g. mydomain.com) will be directed to a specified IP address (the IP address of my laptop, e.g. 192.168.0.42). I need to ensure that my laptop's firewall allows the request, and that the server is configured to handle requests for that domain.