Not really. Once you make an ln invoice and send it to me, I know which one's your node on the network (or atleast a node that you trust your funds with). I then can know every single channel your node has and the capacities in them. I can then sort of guess how much money you might have. But one things for certain - I know all the UTXOs that I need to watch to know which one's might be yours, again not good. As @k00b mentioned, it's bad for the receiver. It's a bit more worse, because with just one ln invoice you reveal your node id and with that all the channels, so you reveal all the UTXOs involved in the funding transactions of those channels. To get around this, you could have a "proxy" node that creates the invoice and recieves payment and then "forward" those sats to your actual node - it obviously gets a bit more involved.

But yeah, as you mentioned if you just use lightning for ever, it doesn't matter. That funding transaction can stay as it is and you can recieve and pay indefinitely on LN for years.