OMG, NOOO!!! All will be lost and yo will DIE!!
Seriously, though, I'm fairly certain there is no law against it, and while not the best of ideas, it is doable. But consider the possibilities. What if your primary should malfunction while diving? Without an octo or other secondary, your only choice is to grab your buddy's octo. No great big deal, right? Ascend and end the dive as quickly but safely as possible.
Okay, what if during your dive your buddy should not be paying attention to his gauges and runs out of air? Now his octo is useless to both of you. Your only choice is to buddy breathe. It appears you are just beginning in diving. Do you think you would have the composure and ability to pass a secondary between the 2 of you while ascending without one or both of you holding your breath and suffering a barotrauma?
In the early days of diving, octos were unheard of. Watch a few episodes of Sea Hunt and there's not an octo in sight. But in the end, it's your choice. You don't say where or what type of diving you'd be doing without it. If it is a quarry or lake where you won't be going very deep I might would take the chance. After all, how often do we have to use our secondary air source? If it's a deeper dive in the ocean, I would probably err on the side of caution and wait until my octo is repaired.