That's the idea behind that system. Images imported using Lightroom desktop should be accessible on Lightroom IOS and vice versa. Images taken with the IOS Lightroom camera should automatically transfer to Lightroom desktop if you have it set up properly. Any editing done on either device should have effect on the image. You must be signed in to Lightroom desktop and Lightroom IOS with the same Adobe ID and password.
They do link together when you are signed into the same account, but I am not certain this works in the trial mode. When you use the free version of Lightroom on your phone it does not upload images to the cloud.