If i understand you correct, then you can select presets in Analog Lab plug-in in your DAW but not when you use the DAWs presets selectors. Is that correct?
It's the same in Studio One 3. I don't think Arturia make presets visible/ avaible for the DAWs preset selectors. This may have to do with the powerful browser selection that Arturia have. But i by me it's the same with many other vendors plug-ins, while others do make the presets availble for my DAWs own preset selection system. I don't have any third party plug-ins that have own advanced browser systems, that make presets avaible for my DAWs sytem.
But if you wish, then you should be able to save some kind of DAW presets of your own. But those presets will only be useful in that excact DAW and for example bypass Arturias powerful preset system. Keep in mind that Analog Lab can access other arturia applications presets and that Analog Lab can save other applications presets so to speak. I would use Arturias system unless for speciel presets that for example include DAW effects.