We are naturally drawn to movement, so shaking any button will cause people to notice it more. That however is not necessarily a good thing. It isn't someone noticing it in a good way. You are very likely to annoy or people who are getting their attention drawn to something that they may not want to be looking at. Think of those annoying banner adds that would do things like this.
There are situations where it is useful to draw attention, but those are when you are telling users something useful. The MacOS dock is a good example - if an icon shakes, I know that something has just finished and requires my attention. It one of them constantly shook because author of the software wanted me to use it more, I would simply not use it.
So in short, having a shaking button will draw more attention and might increase conversion rates in the short term, but in the long term you are going to annoy people. You need to decide which is more important to you.
My personal opinion is that you shouldn't, and if I come across a site or app that does it, I will close the page or remove the app.