You can certainly SEO a website that doesn't use a CMS.

The important question is, given the nature of the site, the budget and goals of the client, and the resources you have to work with, is a hard coded HTML website the most practical solution?

Content management systems like WordPress, Drual, and HubSpot exist to make it easy to build and manage a website. Why? Because the overwhelming majority of individuals and businesses who need a website do not have extensive technical resources to be able to create and maintain a complex, highly-customized website.

I'd be willing to bet that your client fits this bill, which means you can probably help stretch their marketing budget further by using a CMS to make your job easier.

Unfortunately, the answer is "it depends".

I do have some recent experience with this for 2 very small sites (one has around 300 indexed URL, the other has around 70), which you may find useful.

In each case, it took just a day or two to get the most important URLs (best rankings, traffic, link authority, etc.) swapped in for their non-https counterparts. However, deeper URLs with little link authority took up to 90 days to be swapped out.

If your most important URLs don't get swapped out in a week or so, I would check these things:

• Make sure you've updated internal links so that they point to the https URLs. You don't want to pass your link authority through 301s anyways.
• Make sure all versions of the site are verified in GWT, setting the https version as the preferred version.
• Make sure your sitemaps (XML and HTML) contain the https versions of your URLs
• Make sure that the https URLs do not have the non-https URL's set as the canonical version.

Hope this helps and good luck!