Not necessarily. If you find a low competition keyword, you can get away with just doing on-page and technical SEO. However, there are some keywords that require a little extra boost from a backlink in order for you to rank, especially if you want to speed up the process. For example, I targeted about 5 keywords for a client of mine a couple of months ago. After a month, I noticed that the rankings were stuck on page 3. Rather than wait and see if it moves, I decided to give my client a backlink from one of my sites, and a couple weeks later, the site jumped from page 3 to position 3 (page 1) for those keywords.
If you can, it's just better to focus on every aspect of SEO.
"SEO is like an enormous clock. It only works if all the little cogs (factors) mesh together". (I'll probably use that line in my revised SEO guide

).