Sort of. You have to manually upload those observations, it’s not autotmatic. Otherwise the app would drain your battery by constantly searching for an internet connection and we decided that wasn’t great. :-)
See this tutorial:
https://forum.inaturalist.org/t/how-to-use-the-inaturalist-mobile-app-without-an-internet-connection/11620
Even when in airplane mode or without internet service, the phone’s GPS antenna(e?) still function. However, with no cell towers or wifi networks to triangulate from, it might take longer for you to get an accurate location.