No. It doesn't appear that your node knows what it is at all, so it doesn't show up in your transaction history whatsoever, as fees paid or otherwise.

From what I understand, when your node sees the payment, it acts as if it is just one hop along the way to route the payment to another destination until it is told by Amboss, "Yeah, about that.. You are actually the destination. Go ahead and keep those sats without forwarding them." That's in the least technical terms possible, mostly because I don't know the technical terms. 🤣