Does a unchargeable battery cause over all performance to slow way down?

Hello rom450,

It's possible the battery can affect performance in some ways. Those are outlined here in this link: iPhone Battery and Performance - Apple Support

The link is for the iPhone, but much of the information can also be applied to the iPad.

These steps here can help with an iPad that won't charge since it's the main issue: If your iPad won't charge - Apple Support

Take care and stay safe.

Yes. A completely discharged battery can sometimes even prevent a Mac from powering on.