This is a terrible idea.
Because, everyone will talk about this. No, you cannot keep it a secret. Everyone knows "who's doing who". People can see the subtle looks, body language, etc. People will talk about you, in some cases, negatively, because they know it isn't cool.
If the 2 parties are overt in their relationship, it creates a nonprofessional environment, which can lead to difficulties with the bosses.
THEN, if the relationship fails. What then? Well, the talk gets worse. The two parties themselves may talk poorly about the other person. Rumors are started. True or false, a bad environment ensues.
Nothing good becomes of this.