Kurt, please tell me a bit more about this procedure. Never did a clean install on Mac on a spare drive, while working on the main one...
In short, you're just using a separate erased drive/partition to install the OS and your apps from scratch.
Can I install the OS on another drive while keeping working on the same computer?
Yes, that's what I do. You can install OS X on as many separate drives/partitions as you have.
What I do is gradually work my way into a new OS. Like right now, I'm still doing all of my real work in Snow Leopard, while on a separate drive mounted in my Mac Pro, I have Mountain Lion installed. That way, I can keep an eye on updates and see how the OS progresses and initial bugs are worked out.
When I was moving from Leopard to Snow Leopard, SL was a complete rewrite to full 64 bit. 10.6.0 was loaded with major issues that made it unusable for production work. Fonts, especially Type 1 PostScript, were a complete mess. ColorSync was way off. It took until 10.6.3 for SL to be ready for real work. But it didn't bother me. I kept working from the main drive in 10.5.x as I kept an eye on SL's progress.
That's what I'm doing with Mountain Lion (I skipped Lion completely). Some tools I need still don't work, or haven't yet been updated for ML. Overall though, it appears to be a very clean OS. So I'm still in watch mode as I continue to use Snow Leopard day-to-day.
How then I migrate all my system to my main drive?
By "system", I presume you mean the rest of your third party apps and personal data? If so, I never move those, either. The purpose is to keep the drive completely clean. I reinstall all apps I use from scratch onto the new OS. I don't want any garbage, damaged files, old OS files or prefs brought over. The few I will copy from my current drive is things like all of the preference files from my user account for the Adobe apps so I don't have to set all of my palettes and preferred settings all over again. Otherwise, pretty much everything else gets left behind.
Will I be able to restore files from Time Machine from a backup that was made in Leopard? (just in case)...
You can, but I don't use Time Machine, so can't say exactly how that would work. If it just copies over everything that doesn't exist onto the new OS, then you've defeated the purpose of leaving old, outdated, or possibly corrupt data behind. Pick and choose from the TM backup to only bring in what is absolutely necessary. Which of course is any files you've created, your email data and other specific items. That does mean though that you need to know where this stuff is in the first place. Rather hard to do if you don't.