I've done quite a bit of reading on the qbo. From what I've gathered, it doesn't quite work that way. I used to think of it in a very similar way. So I understand where you're coming from. Think of it as more of a modulator not so much as a driver. Which can constructively or destructively interfere with, well many various things allegedly. It's actually quite complicated. However, it's starting to be revealed to be quite important. Definitely not fully understood, and is a hot topic of recent and further research. Most notably in more recent research, it has a strong connection with how the mjo is able to propagate, it's amplitude, and ability to have effectiveness. This happens only during boreal winter and is strongly linked.
So, for example, we have a la Niña plus EQBO. Research says that because of this, the MJO should be more active. Also, it should be able make it beyond the Maritime Continent barrier. While, under WQBO plus la Niña, that would be the opposite. If it were an el nino, it wouldn't matter for the MJO. But also, the MJO is less effective in those cases. This is just one example, it goes beyond the MJO as well. The MJO relationship has just been the focal point more recently. Here's one recent paper which goes over some of this. Hopefully this is somewhat useful information for you.
https://www.tandfonline.com/doi/full/10.1080/16742834.2019.1588064