It doesn't appear that this is supported in the SDK. The programmer's guide only gives information on how to link an invoice to a sales order. Since the LinkToTxnIDList does not give an option for what type of transaction type it is, I would guess that it is only looking for SalesOrders when supplying the ID. I also tested linking by specifying the individual line item ID and still get the same error.
Perhaps as a workaround, you could create a SalesOrder from the Estimate (assuming that you can link them), and then create an invoice from the SalesOrder.