Exactly. Most overdrives are attempts to sound like a cranked amp. There's different utility for other overdrives (like a tubescreamer providing a mid boost for a solo), but in general, the sound of a transparent overdrive is just the sound of your amp barely breaking up.
Also, I agree with your earlier comment - if you're committed to using one of the overdrives, the Teemah is probably the clearest in my opinion. I also use the Kinky Boost in a similar way that probably echoes our thoughts on amp breakup - ideally, the boost just pushes the amp a little harder and gets that nice breakup.