I would say that you would probably have to dump the cracked version first and then sync the new one on right afterwards.
Just an FYI, we don't talk about cracked apps here at EIC. We don't like illegally obtained software. But since you are doing the right thing and buying the app, that's cool.
If you have it on your computer then when you go to purchase the app it will tell you that you already purchased it, this goes for updates as well, updates will be free in the application section of iTunes. To legitmately purchase the app you must delete it from your iPhone and also hunt down the .ipa file via finder on your computer (/User/Music/iTunes/Mobile Applications) and delete it there. Then iTunes will no longer believe you own the app and you may purchase it.
Oh and for those wondering why he may be wanting to purchase an app he already downloaded for free, that was the intent behind Kyeks creation of Appulous. It is a way for people to test apps so they don't get burned with purchasing buggy or crappy ones.