The simple answer is no – search engine submission isn’t necessary. Every search engine today can crawl and index pages by following links. A single inbound link from any already-indexed page will identify your page to the engine and if that page links to other pages within your site, they will also be indexed… and so on.
This is one reason inbound links are very important. (In fact, acquiring back-links may be the most important of SEO.) In theory though, a website owner shouldn’t have to ’scout’ or ‘hunt’ for links. If the content you’ve written is of interest, useful, and/or important, there is a natural tendency among web users to link to information.
That said, submitting your site to search engines that allow you do to so can’t hurt. It only entails about 5 minutes of added work. Once is enough – you don’t need to submit your site more than once. It doesn’t help or get your site crawled any quicker or more often.
Submitting your site to most search engines doesn’t cost a fee. There are exceptions, and these are usually industry specific search engines.