The short answer is that communication and processes drive collaboration between teams. Where communication is clear and frequent, the need for well-defined processes diminishes (and vice versa). You have to factor in time no matter which approach you take for the project (even a combination of the two), it is just something that is done upfront or distributed throughout the duration of the project.
This is an interesting approach to building a commercial website. Even though it might not be hard to reverse engineer the sitemap, I think it would be quite difficult to understand all the different paths for user/task flow unless you have a very good understanding of the business or if it is comprised of very linear and simple transactions.
However, having been assigned this task, in response to your questions:
Can we start working on wireframes and visuals without content? Is there a best practice for that to minimize the hassle of the process?
Yes, you can. The wireframes are intended to provide you with a starting point or the structure of the pages that you are going to create, and the content allows you to customize and refine the design to suit client (assuming this is different to the competitor). You may choose to factor in some of the limitations or constraints from the outside (in which case you need content upfront), otherwise allow time to make adjustments to the design when they become available.
I would definitely push back on handing over any design that has been created without checking against the content, since it will usually cater for an ideal scenario and not the worst case scenario that you need to allow for.
If both the digital agency and content agency are working at the same time, what kind of deliverables or documents should be provided to each assuming the content agency doesn't have a content strategist?
It is not uncommon for writing style guidelines to be included as part of the branding standard/guidelines. However, this might not cover digital content requirements (at least not explicitly) and therefore you need to adapt this information to the client's needs. In addition, there may be a standard set of terms that should be used, or if they are not user friendly then you need a way to map business terms to user terms so that they can be applied consistently.
Also, if they do not know the domain area for the business, it is also common to provide one or more subject matter experts that can help with creating content or can contribute general or technical information to help the copywriter.
If you want the content to also be SEO friendly (which the content strategist can advise on), then you probably also want some analytics data or existing research on the key demographics or target audience as well.