Yes, you are correct in your analysis.
Setting the common mode of the inputs to 2.5V allows the use of the full input range for single-ended inputs since the AINP can swing from 5V to ground, thus achieving a =/-2.5V signal. If you do this, depending on what your input signal is, you may to level shift the AINP signal. Make sure that the DC levels match otherwise you may not have a perfectly symmetrical input range.
