You might be planning to launch your website with a completely new design in order to give it a face lift.  Your concern is whether the search engine optimization  process you have adopted would still be applicable and can give the same results that it produced earlier? You require reassessment by the search engine of your new site.

Redesigning the site for improving it is always a good idea.  In fact there should be periodical redesigning of sites.  New expectations are developed and you will get a chance to address the issues that have been kept aside relating to the design you originally adopted for your site. 

If the redesigning is properly done it will inform the search engine that your site is still there and is very much active.  In truth such redesigning, if made compatible with the search engine requirements, can really boost up your site prospects.

When your side has already been indexed on the search engines, once you redesign your site it would automatically spider you.  However, for substantial changes you must contact the search engines and directories and request an update. Otherwise it may so happen that the search engine might not recognize your site any more and do no more figures on the seo result pages. In result you may loose substantial business even if such absence from result pages is for few days only.