Independent research on the academic benefits of the Advanced Placement English Language and Composition course indicates that not all students receive academic benefits from participating in the course. In a study with a sample size of over 90,000, the authors found that students who took the AP English Language and Composition course did not receive any increase in academic achievement unless they also prepared for and took the AP test. The authors controlled for over 70 intervening variables and found that AP students who took and passed the English Composition and Literature exam had ACT scores that were points higher than non-AP students or AP English students who did not take their course's AP test.  This led the authors to state that AP participation "... is not beneficial to students who merely enroll in the courses ..."  :p. 414
Since I have just the other day taken the DELF B1 exam and Assimil was my primary method (and thank you for detailing the instructions in this page as they did help) I thought I would offer how I thought of this method, as I was always looking for someone’s review of someone who had finished Assimil and how and if it worked for them. So here goes:
Firstly, if you are serious about language learning, Assimil is indispensable. I had learned first with Hugo French in 3 months and that established the grammar aspect of my French journey (Contrary to most, I actually really enjoy grammar!). Therefore, I do think as you said above Josh, that a grammar book should be a supplement to the course.
Not sure how much you travel around the language learning community but with Assimil I (after a long process) combined methods of 3 polylglots. Luca and his full circle method; Professor Arguelles with shadowing; and Tim Doner with his comments on immersion, constantly thinking in your target language as much as you can, creating conversations, etc. I’ve studied French for 7 months and I discovered the language community about 5 months in (3 months of Assimil) and eventually created this method for myself in the start of the 6th month. When I had this ‘lightbulb’ moment idea, the next few weeks were pretty painful! After realising I should use this strategy for French from now on I had to shadow 7+lessons a day in preparation for the DELF, rewrite them at times, and review them. And add to that, thinking in the language. The most difficult aspect I think of language learning, isn’t memorising vocabulary or shadowing lessons, it’s becoming creative with this new material. Despite being able to recite from memory 70+ lessons, it’s difficult to adapt that in a real-time conversation which is what happened during the DELF. I was nearly 5 minutes late, and stressed out from traffic but regardless I don’t believe (for me) Assimil really prepares you for interaction at a B1 level if you haven’t practiced before with natives. I had a French tutor who I seen now and then, but within a conversation it is difficult to make your brain ‘click’ and run smoothly if you haven’t used it ‘creatively’ in the past. Which is why I believe that if you use Assimil, then with talking to natives it is possible to reach within the boundaries of B1 oral production. I would love to talk to someone who got to B2 using Assimil solely as their only resource.
However, I believe that by utilising Assimil with interaction with native speakers (I would say that’s the most important) quite regularly, reading articles and adding vocabulary from that then you will reach B1. I do believe B1 reading comprehension with Assimil is likely if you choose to add some vocabulary from news articles into an Anki deck or some other SRS. Oral comprehension, for me, Assimil doesn’t solely prepare you. Rhythms change, different speakers, different vocabulary, LingQ would probably be a good addition (which I have only just recently signed up for). As for written production, for the DELF at least, you could be faced with topics on the environment or some other slightly abstract topic, which in the 113 lessons of Assimil: New French with Ease, there is rarely any mention.
So, in summary (after this very long post!) Assimil should be your best friend with languages. You should become overly familiar to the point where you can recite a high amount of the lessons or at least know their translations. Will it get you to B2? For me, no. Will it get you to B1? If used alongside a grammar book, Anki and (most importantly) interacting with native speakers. Yes, I really believe you’ll get there.