I have an app on the market that requires sdk 2.0 I want to rewrite and publish it using 1.6 to find a wider audience.
The question is: if I update my already published app with an sdk downgrade to 1.6 will it then show up to users with phones at 1.6? I know currently the market search shows my app only to those that have 2.0 phones.
Yes it should work fine, exactly as you describe. Phones running 1.6 will suddenly be able to find your app when they search in the market.
This isn't really an answer to your question, as mbaird has already taken care of that, but ut will hopefully still be useful information for you. I'd have put it in the comments box, but it was a bit too long...
It'd be even better if you could downgrade to Android v1.5 as one of the popular early Android phones, the HTC Hero, hasn't officially been upgraded yet*. According to statistics collected in January, about 1/3rd of Android phones were still running v1.5 (see the Android Developer's "Target Devices" page). If you only want to use 1.6 for the support for multiple screens, and not the libraries it includes (e.g. advanced gesture recognition), then there's a trick you can use described on the "Supporting Multiple Screens" page which explains how to develop your app 'targeting' v1.6, but remaining compatible with v1.5.
*: However, according to Engadget the official upgrade should only be just over a month away.