No, the pad light indicates that the receiver is positioned over the pad properly and is drawing power from it. If the receiver isn't properly connected to the battery, usually through little contacts next to the battery (or, in a sleeve, to the microUSB connector), the phone won't charge. If you've ever had any problem with the connector, like you have to move the charging cord to make the phone charge, that's the problem and it has to be fixed inside the phone.
(The charging light on the phone should stay lit even long after the battery is fully charged. It doesn't indicate that the battery is accepting a charge, only that charging voltage is being sent to the charging circuit.)
If the bare phone, resting on the pad, doesn't give you a light on the pad, move it around until it does. For instance, a Note 3 on a Lugu Lake charging pad has to be about 1/2" right of center, and slightly off the front edge of the pad, to charge. Every combination of phone, receiver and pad is going to be different, so move your phone around. If you're using a receiver that you put into the phone on top of the battery, tear off about 3.4" of transparent tape and stick it somewhere clean so you can grab it easily. Then position the receiver until you feel the points fall into place with the dots ion the phone. Take the tape and tape the receiver to the phone in a way that you can lift the receiver (with the tape as a hinge) to get the battery out without disturbing the receiver location.