Unclear.
I would guess that if the secret-keeper is giving up the information willingly and aware that they are giving it to the recipient of the memory then they should become aware.
The Fidelius Charm is not without its weaknesses. If the Secret Keeper wishes to do so, they may divulge the information at any time (although the secret cannot be forced, bewitched or tortured out of a Secret Keeper who does not wish to give up their secret; it must be given voluntarily). If the Secret Keeper dies, anyone to whom he or she has confided the information will become a Secret Keeper. This could involve many people, any of whom might be more willing to share the secret.
- Secret Keeper - Pottermore
To me this implies that the secret keeper may pass on the secret at any time in any way
that they find fitting (whether this be a letter a Pensieve face to face etc.) Since charms exist where it cant be given involuntarily, my best guess is that this applies to accidents as well, so, I think the Secret-Keeper would have to be aware and willing to divulge the information but if they were both of these things than I believe that yes, if someone wanted to they could pass on the secret via Pensieve but if it was an accident then the secret would not appear in the memory. This is all pretty cryptic magic though and I cant be sure of this.
Update: I also believe that it would be impossible for a non-secret-keeper to create a memory of the secret.
If the Secret Keeper shares the hidden information, the person to whom he or she has confided it will be bound by the Fidelius Charm and find it impossible to pass the information on.
- Secret Keeper - Pottermore
To me the most straightforward way to prevent sharing a memory of the secret would be that the secret would either be unextractable (by some means of magic) or that if someone did manage to get a hold of it that it would blot itself out (like how memories can be tampered with by wizards but this would be simply by the rules of the Fidelius Charm).