Will two 12V LED light strips run off the same source at full potential if the wires are spliced and connected?

Unfortunately, there is not provided enough information to adequately answer your question.

First, the amperage capacity of the power supply must be stated; if it is barely enough to operate one light strip, it will most likely not be able to provide power for two.

Second, the power requirement of each light strip needs to be stated. Using that will determine what will be the total power requirement when they are connected in parallel.

For example, if one light strip requires 2 amps at 5 VDC, then two light strips together (in parallel), will need 4 amps at 5 VDC. If the power supply cannot provide at lest 5.5 amps continuously, then a larger power supply will be required.

NOTE: the numbers used above are only used to show an example of electrical current requirements.