Hi GSlayerBrian,
I have some suggestions/comments about your description. First and very important, you can NOT connect 2 power supplies at the same contact points expecting to get a voltage increase. The reason is that both power supplies, in this case the LiPo battery and the power supply cable, have different output voltage, even if both power supplies have the same output voltage is not recommended either. To do this kind of connection you must connect the power supplies as serial connection, not as parallel connection. So be careful with that.
About your voltage regulator, I searched the datasheet of the LM2596: LM2596 DataSheet and I checked the output voltage is not a function of the input voltage, so you could connect for example 9V, 12V or 18V in the input and you will still having the same level output, 5V in this case. You can check it with a voltmeter to make sure. But again, be careful how you connect both power supplies.
Now, my recommendation to you is to use a 5V relay as following: In the normal state of the relay, the LiPo battery will be supplying the Board, when you plug the 5V power supply cable the relay will switch and then, the power supply cable will be supplying the board while the battery is disconnected. When you unplug the power supply cable the relay will switch again into its normal state connecting the LiPo battery. So the board always be connected to one of the two power supply. But, there is a little detail that I'm not sure. When the relay switches between each state there will be a very short time (really short) when the Intel® Galileo Board will be without any power supply. I don't know if that time will be short enough to become unnoticed by the Galileo. So, I suggest you to try to use an oscilloscope to measure this time between relay changes before you connect it to the board.
Let us know if this help you. Have a nice day!
Regards,
Diego.