The answer to your question is: yes, it is possible to to separate the soul or jivatma from the body. Even one can enter another body through this process:
When the bonds of the mind caused by action have been loosened, one may enter the body of another by knowledge of how the nerve-currents function. [PYS - 3.37]
But from your question it seems you have some wrong information about yoga which needs to be corrected.
First is, yoga is that state where all the activity of the mind ceases (PYS - 1.2). So the idea that in yoga one must be somewhere thinking something is incorrect. If one is thinking something then he might be practicing yoga, but he is not in yoga.
And secondly, not only detaching the soul, but there are other such siddhis (skills) which automatically arise when one practices yoga. Even one can go to other planes of existence and interact with other beings. But all these are not the purpose of yoga and are simply obstacles on the way because the yogi may get diverted from the true purpose on the achievement of these things:
To the outward turned mind, the sensory organs are perfections, but are obstacles to realization. [PYS - 3.36]
Regarding how does it feel, I have not felt it but it can't be expressed just like we can't express how sweetness feels, it has to be felt by oneself. And by freeing the soul from the body the yogis can achieve moksha voluntarily or go to the plane of existence they would like. There are many examples of such saints and yogis in puranas.
Now regarding differentiating yoga from dream, you don't need to use a totem as they did in the movie Inception (just kidding); you would be able to know it yourself. How? Because there are four fundamental states that a jiva goes through, wakefulness, dream, sleep and turiya. Apart from the last state, every other state is simply not yoga. And just like you are able to differentiate wakefulness from sleep and dream, you will be able to differentiate the state of yoga.
On a sidenote, it is better to know and learn about Yoga from a qualified teacher. Forming ideas by listening to and reading text of unqualified persons can be harmful. The Patanjali Yoga Sutras has a lot of information in a condensed form. One can know the right things by understanding it from a guru.