(Theory) Did Emil poison *spoiler*?

Ever since I've seen the show, I've had this theory about Emil. Did he poison and kill kaiser Reinhard?

I have several reasons for this, the first is that Reinhard only starts to get sick AFTER Emil shows up. Secondly, we know that Emil has medical expertise, even though he still is in training he is clearly qualified enough to be the kaisers personal aid, so he could disguise a slow poisoning as an illness.

What would be the motivation behind this? We know that Emil's parents died during the battle of Astate, perhaps it is revenge for the death of his parents.

So that's just a theory that's been on mind, I am actually more curious about what you all think!