While it won't completely derail it, mis-clicks will slow down your new pup's learning. From AKC:
The clicker or marker communicates the exact moment your dog does what
you want. The timing of the click is essential and every click must be
followed by a reward.
A good way to get a feel for what it's like to learn from clicker training and build empathy for your pup is an activity called "train the trainer". Get a pile of stuff together in a room, decide on an action you want your wife to perform with an item or items, and then using clicks only try to train her to do it by clicking when she gets closer to the goal action. Once done, swap roles, and maybe even try with your child. You'll quickly learn that mis-clicks are serious misdirections! And some people (like some dogs) will offer more behaviors to succeed, while others are more tentative with their attempts, so mis-clicks will affect different dogs differently.
As the AKC noted, you want the click to guarantee that a reward is incoming, so mis-clicks will lead to either a mixed message on what the click means (is it a treat? or is it not?) or to rewards for the wrong thing. The first may make your pup less willing to offer behaviors, the second might make them confused about what you want.
For best success, treat a click like it is law. Of course, mistakes will be made but try to minimize them!
With regards to your child, I'd keep the clicker for training sessions with the grown-ups. You can have your child practice known skills (rather than try to shape new ones) and use a verbal marker (like "yes!") that you can treat a bit more loosely.