As it happens I'm currently working on a Commerce Server implementation that uses cart functionality without online purchasing functionality. As such, the build in engagement plans didn't make sense so I didn't add them to the site. The problem came in the form of an error when adding items to the cart:

{"Errors":["AddCartLine: Engagement automation plan with name Abandoned Carts cannot be found."],"HasErrors":true,"Success":false,"ContentEncoding":null,"ContentType":null,"Data":null,"JsonRequestBehavior":1,"MaxJsonLength":null,"RecursionLimit":null}

After search around for the pipeline that was adding this, I found the Sitecore.Commerce.Connect.CommerceServer.Orders.Pipelines.AddLinesToCart processor that has a "DisableEap" property, setting this to True resolved the error.

<configuration xmlns:patch="http://www.sitecore.net/xmlconfig/">
  <sitecore>
    <pipelines>
      <commerce.carts.addCartLines>
        <processor patch:before="processor[@type='Sitecore.Commerce.Pipelines.Carts.Common.RunSaveCart, Sitecore.Commerce']" type="Sitecore.Commerce.Connect.CommerceServer.Orders.Pipelines.AddLinesToCart, Sitecore.Commerce.Connect.CommerceServer" >
          <param desc="Rollup">True</param>
          <param ref="eaPlanProvider"/>
          <param ref="eaStateCartRepository"/>
          <param desc="DisableEap">True</param>
        </processor>
      </commerce.carts.addCartLines>
    </pipelines>
  </sitecore>
</configuration>