In the first stage of fermentation it could be some good. Yeast needs oxygen to the growth phase, when building membrane and other things needed to increase the cell count. When this oxygen is over, then the yeast can take its anaerobian way, and produce alcohol and carbon dioxide, which is needed for beer making.
But if you shake your wort vigorously some seconds/splash it to your fermentor before you leave it alone, you get a good enough amount of oxygen.
If you never stop agitating it, maybe it could over-oxygenate your brew, or oxygenate after complete atenuation - don't know if it makes sense considering a very leak proof fermentor; after some time the whole atmosfery of the fermentor would be carbon dioxide, considering that tight environment. But any oxygen after the end of fermentation could feed beer spoilers that you don't want. And I don't know what would happen to your alcohol production.
But nonetheless, you want to settle solid things of your wort, including dead/inactive yeast cells. So, even if it was good to yeast growth phase, you would need to leave it alone after that.
So I think it is a bad idea. If it is a matter of space, you could put a shelf above your machine, or build a rack that envolve it like an outside frame but don't touch it. Good luck!