Kinda correct.
Depending on your lesson load and style of learning it is very possible you will do kanji and radicals at the same time. At the lower levels it might be all radicals first but after level 10 it drops off. As soon as you level up you will be able to learn the radicals and unlocked kanji for the new level but it’s up to you and your leveling style.
It’s entirely possible to follow a different level up style and still have no pending vocabulary by the time you level up. But that usually requires fast style of leveling.
Although the wait times are set the method in which you study wanikani is really up to you.
btw have you read the official and unofficial guide to wanikani. I think that would clear up a lot of your questions. Here is the link to the unofficial FAQ which contains links to the official guide and FAQ.