James Fuller: it may affect but that doesn`t mean you will lose rankings. Your rankings will be affected mostly if you change the content and structure of your website. WordPress is searchable by search engines.
Lisa Brown: I migrated a site from Wix to WordPress 2 1/2 weeks ago, their rankings are already improving. We did redirects for every URL on the original Wix site, added schema, in addition to brand new longer content.