For initial testing in IE this may be sufficient, but there will always be some differences between how a site loads in an emulator to the real thing. The amount of testing you do should really be strategically influenced by the target user base and the amount of traffic the site receives.
By using a web analytics tool such as Google Analytics or Piwik (many others exist) you can identify the operating systems and web browser versions being used by those visiting the website. If only 8% of your visitors are using IE 7 then it would make sense to commit 8% of your testing time to IE 7.
If the site needs to be 100% guaranteed tested as functionally working and appearing properly then a more formal and rigorous testing approach is required which would involve systematically checking each functional feature on each page in each version of each web browser you will be supporting. Somewhere along the lines though you will have to make a decision as to which browser versions you will support since otherwise you can waste significant amounts of time testing on older browsers.
From experience I tend to find that if I commit time to ensuring a website is fully compliant with W3C XHTML and CSS standards (with the exception of mobile clients seeing the inclusion of a few HTML5 tags and attributes), then generally the presentation of the site is normally consistent across browsers these days.
Of course don't forget to test on a selection of browsers, not just IE. For desktop users, the dominant web browsers are IE, Firefox, Chrome and Safari, while for mobile/tablet users the dominant web browsers are Safari, Android Browser, Chrome and Opera Mini.