Does a Daikin AC remember the settings when it was last turned on, or what the remote is set to on power-on?
I read the manual for your AC and it did not contain any information which could answer your question. I will guess and say that your AC will remember the "Intelligent eye" setting through a power cycle.

Why not just use your Universal Remote to turn the AC off and on and see how it behaves? There is an "Intelligent eye" indicator on the cooling unit so you can quickly see what mode the AC is in.

You don't give any details on the Universal Remote you are using, but the ones I am familiar with tend to be programmable. So if you do need the Universal Remote to send a command to set the "Intelligent eye" feature on, you should be able to program the UR to do so.