No, your computer will not first attempt to look within your home network for that address. It will look at the routing table.
That table contains rules for the following things
- Does the IP match an explicitly IP (added with route add -net). Then send it out via this interface
- Does the IP belong to a network range listed, then send it out over a specific interface.
- If all fails, then send it out to the default gateway via specified interface.
There is no specific 'internal' vs external' network here in the table.
Typical setups with a single NICm switch and router however usually fill those tables as follows:
- If it is for myself (localhost 127.x range or own IP) then send it 'out' via the loopback device.
- If it is for the local network (which it knows since you set up a NIC with both IP address and network mask) then send it out via the local ethernet.
- If it does not match that then send it to the default gateway (aka your router on the local network).
The computer does not care how the packet arrives at its destination. All it knows, and all it needs to know is what to do locally and delegate the rest.
This might resemble your question a lot, but it is not the packet which know how to travel. It is the local computer, using local routing tables, which decides what should be done with the packet.
Now if you set your internal network to 74.125.224.X and try to ping (with updated routing tables) the network stack would recognise you are trying to ping your own IP. You would get an answer to the ping from your own computer. Since you are not google you can forget googling around for answers via the search engine. It would never reach the real google computers.
Communication with them would be impossible, since packets for them would never leave your computer. Instead they will be routed right back via loopback.
Should you disable loopback or tell your computer explicitly to push those packets towards the default router and the internet then you would not get an answer. All other computers still forward their package to the real computer at google, and not toward your network.