Is it possible to leave the Silent Realm without completing the trial

Yes. Skyward Sword games saves can be copied to an SD card. They take up one block of memory.

Keep in mind that that game saves are locked to your region. From Wii Save:

We're nearly positive you can't use foreign saves on your Wii. We're still looking in to a way to do it, but so far, it's not looking good. You'll most likely have to stick to your own region when swapping saves.

As long as the Wii you use is in the same region as your Wii at home, you should be fine.

I've downloaded a couple of Wii save files from that site, and never had a problem. I've never tried to copy between consoles, though. When copying saves, you have to delete any existing save files from the destination before the Wii will copy anything. It won't overwrite.

From this thread:

Later during the game you will be able to revisit silent realms you've completed.

If you need the dusk relic treasure, there is a Sheikah Stone in a cave in Skyloft (the first cave you go to find your Loftwing). There should be a flock of butterflies there. Play your harp and a Sheikah stone will emerge and will sell any treasure you want.

Bring lots of money though, they're 100 Rupees each.