Appearently, it's possible to do this. But I wouldn't recommend because of the following reasons:
It's too far. According to the video, the other End islands are about 1,000 blocks away.
Use it at your own risk! This could be dangerous and you may fall into the Void because of this.
There are a few ways to get across.
Not recommended, but you may try. Build far away from the center island into the other islands.
Make a machine. This requires a few redstone blocks, sticky and non sticky pistons, glass, and slime blocks. Use it to get across.
I have tried going to the island with killing the Dragon by flying in Creative and of course I found them. So it's possible, but has a lot of disadvantages to it. I would recommend killing the Ender Dragon and then go to the portal to the End Cities.
Basically, the End Gateway you get when killing the Dragon teleports you to the outer islands and is faster.