Not necessarily. There's no need to break the encryption or have logs if the NSA can monitor all the traffic going in and out of the proxy server. They just have to correlate your incoming encrypted connection with the outgoing unencrypted data to remove the layer of anonymity. I'd frankly be a little surprised if they weren't doing this or something like it.
I would guess that using PIA makes you less secure against NSA snooping since it makes you more of a target and provides weak anonymity.
