Tenzin and Lin could discuss it together, but they can't exactly do more than question Asami, who may be unlikely to divulge Xana and Xano's bending bestowal. They're helping save her company and gave her the opportunity of a lifetime, so betraying them by reporting it to Lin and Tenzin may go against her. I think, in time, she may break enough to admit it to Mako in confidence, who is also likely a detective/cop at the time but her loving boyfriend (here's hoping anyway). Any side effects you can think of? I think fatigue may be one; Korra has the spiritual advantage and the past lives to help guide her, something that Asami won't, so creating a new Avatar would likely pose problems. I think Xano would be crazy enough to hit up Korra's dear old uncle about helping Asami access the spiritual side if possible. Who knows how far this ambition will go.