(psi - I admire your ability to construct music in your head. Did you build this in time? I have plenty of time everywhere, but unfortunately I have to be at the keyboard to do something. Maybe this comes with experience?)
Yep, definitely. The basic rule is simple, you'll start from 0 as everybody and get better with it (and great eventually) over time. You can start doing it by doing sort(er) sessions and (very) simple structures. Also layer the channels in your head, as you would do with the tracker too, work on separate times on the melody, bass, percussion, etc. One of the most awesome fact about this technique is, that you can create about any sound you can imagine in an instant (yea, reproducing it with synths afterwards needs further sound engineering technical skill). Also you can try many takes, editing and experiments with songs or on the part of them, over very short amount of time, without any "workarounds" that you would do while tracking. So after you found the flow that work best for you, you can write it physically on the tracker, saving you a considerable value of production time. Over time, you will be able to "hear" the sounds that you create more saturated and crisp, you will learn how to modulate them, also you will able to build and change song structures faster, and layer more parallel channels.
Lets see.... a good exercise would be, rather than starting from scratch composing, is to try and reproduce any of the song that is already made, as accurately as you can. Try to remember how those sounds in it sounded like and mimic them, do the same with the structure. You dont have to focus on all the layers, just try to get roughly close. If you are satisfied after a couple of tries, then try to change something on them (sound or structure wise). This simple little trick can ignite a creative rush easily.
A different, but related technique (that i'm using sometimes) is to use your time when you dream to compose while you can. When we're dreaming, our brains works a bit differently than in waked state, so there is a good chance that you will figure out some good melody or song structures that you wouldn't think of otherwise in normal state. Our brain focuses a lot more to basic emotions also while dreaming, thus making it easier to ignite that creative spark that you may be looking for at that moment.
Yea, our mere natural bodies are a terrific technical tools in a lot more ways that one would think of, even in this modern world. I'm using modern world technology only to aid me with composing, and help me able to reproduce, record that i've imagined over time, as accurately and fast as possible, and not trying to replace in any way the already given natural (and mobile) ability, that our brain functions can provide.