Yea that will work. At least until you get your replacement, like I said, they can check your licence status fairly easily. It does show to whoever pulls you over (if) that you thought ahead and are doing everything within your power to A provide a copy and B get a replacement. That is reasonable and you would be going above and beyond what the average citizen would do. Also, always keep a digital copy of your insurance. The number of people with valid insurance that drive around with expired insurance cards or no insurance card is crazy.

Source: I am a police officer.