Is it wrong to charge a laptop/cellphone battery when the device is on?
There are SOME things that won't operate while you are charging them. My nice Sony noise-cancelling Blue-Tooth headphones just automatically power down when you plug in the USB cable to charge them.

But most things will continue to operate if you plug them in to charge the battery. Most (all?) cell phones I've ever seen. Certainly there are those of us who have no land-line (only cell phones) who depend on our phones operating even when we are at home (or at the office, or in the car) and charging.

Now, some equipment may charge more slowly during operating, because some of the power you are putting into it goes towards actually operating the gadget.  But unless there is an explicit warning or automatic behavior, IMHO, it is safe to assume that you can continue operating something during charging.