In our agency we always recommend and perform an SEO audit for all new clients. Without understanding clearly what is technically wrong with the website, no amount of off-site SEO is going to work well. A technical SEO audit will be able to highlight areas where the website is struggling, where it could be improved and what it is doing right.
An SEO audit is all about getting the website onsite SEO right. I describe it to potential clients as the foundations of a building. If they are shaky and not planted firmly in the ground then building on top of them will not be secure or long term.