Acquire can fully perform without having code on site. However, we recommend adding code on site for several reasons:
Having code on site allows Acquire to have more visibility into what is occurring once the customer enters the website. This means that the account can be optimized for actual conversions on site, and targeting can be changed so as to drive qualified and relevant traffic to the website, instead of simply for clicks. This is only possible only with code on site. Eventually having code on site will also allow us to run retargeting campaigns.
Related article: How does Aquire track conversions?