Does the number of network connections used by a VidiU Pro affect my Sharelink subscription?

No.

The Sharelink subscription level is not related to or affected by the number of network connections -- USB, iPhone or iPad, Wi-Fi, or Ethernet -- used on the VidiU Pro.

The cost of the Sharelink subscription remains the same for each VidiU Pro unit, regardless of how many or how few connections you are using when Sharelink is enabled.

The required Sharelink subscription level is determined by the number of VidiU Pro units that are simultaneously streaming with a single Sharelink ID.

Please see these articles for more information:

How Many Sharelink Subscriptions Do I Need For My VidiU Pro?

How Many Connections Can I Use With Sharelink At The Same Time?