Can an iPad work if it doesn't have a dedicated line?

Yes, it can still be used on WiFi. An iPad does not require cellular service. This forum is not customer support. No one here has access to your account. We have no idea if you have a line for each iPad. Look at your bill.

Why do I see specific (individual) phone numbers listed for the iPads I have on my account?  Does simply having a number assigned to the device necessarily mean I ma paying for an additional line?  I realize you are not customer support, but while I'm waiting in line for them, I thought I would ask if anyone knows the answer to that question.  THanks.

Every line is assigned a number, even if it is for an iPad. An iPad line is for cellular data only. If you see a line on your account for each iPad then yes, you are paying for each line.