OFC they will, it would be criminally negligent of them not to.
However if the NSA is currently your adversary and you are worried of being targeted then pre QC or post QC encryption isn't going to matter push comes to shove they'll beat it out of you.
But as I said if the NSA or any other agency is currently capturing and storing encrypted data they can't afford to decrypt via targeted means they'll be able to retroactively decrypt it if they do manage to build a quantum computer and quantum supremacy would be a definite thing.
But right now there isn't an encryption the NSA can't break as long as there are people and additional assets involved in the process.
In fact I would be that for targeted attacks it would still bet easier to bribe, raid/hack the server farm or beat the snot out of someone in a black site than to use a quantum computer for quite a while after these things would be become a reality to factor the RSA private key corresponding with the key exchange of the traffic you want to decrypt.
