Hi,
Your local server should be able to contact Google's C2DM server, but that won't be a problem.
Apart from that your Android devices should be able to contact your local server, this can be
1. when your Android devices are within the same (local) network as your server
2. you make your server accessible from the internet. This implies configuring your modem/router so that an incomming connection (eg: port 80 = http) maps to your local server within your network (check with your provider whether incomming connections are allowed and also which ports: there are some providers blocking incomming connections on well-know ports such as 25 (smtp), 80 (http), 443 (https), ...).
If you have a dynamic IP you will also need a Dynamic DNS services (such as dyndns, no-ip, rollernet, ...)