The answer is: no, you can’t.
For me, TortoiseGit is a tool that you can use to make the transition from – in your case – CVS to Git easier (like I wrote in my answer to Does TortoiseGit actually make Git a lot easier to use like TortoiseSVN?). But once the transition is made and your colleagues get more familiar to Git, it’s time to come up with the real tools.
And the most powerful tool to interact with Git is the command line. Period. The Git Gui and gitk are also usable, bring some convenience but lack explorer integration (at least in terms of overlays). But in times with multi headed development boxes: why don’t keep the Git Gui open on one monitor (the one used for general management stuff) and work on the other?
I recently also did an introduction to Git in my team at work. We were used to TortoiseSVN, so I also showed them how to add files using Tortoise, how to commit and so on. But on every slide, I also noted what they have to type in the Git Bash to achieve the same result. That way, once they’re a little more experienced, they can take out the introduction slides and peek at the commands they have to use.