Probably not. In the character creation, Boochbeard points out that your parents are dead. If you got Lucky Jack Russell from the Presidio, maybe you might because Gandry says they might be trapped in a dungeon somewhere.
When do I get to see my parents? is there a certain level? do they join my crew? do I ever see them?
Welcome to the message boards, if you haven't been welcomed yet, Alexander. As you progress through the game there will be clues as to where they should be, or where we can hopefully expect them to be, well their graves, that is. It is hard to really pin down at this point as Blind Mew is a master of making us delighted with his snippets of information as he dangles them enticingly for our enjoyment.
I hate to break this to you, but your player character's parents are deceased when you start the game. You will hear their voices in the crystal cave, while qualifying to meet Gortez. There they ask you to visit their grave in El Dorado. I expect that you will get Mom's map piece in a future expansion. Your pirate should cherish the direct memory of them while he has it.
Anyway, isn't it that in Aquila while doing one quest (warning:spoiler!), you lose memory of your parents? First 5 years if i recall correctly. And besides, they died, so only way to see them is not an option i would like for my pirate. Only if Old Scratch can do his magic and show them to us as ghosts. But i have to agree, it would be nice to finally meet them in some way.
My theory is that our parent's graves may have some part to play when we reach El Dorado. I don't think they're still alive, but maybe they left some kind of message for us at El Dorado, or some sort of information on the Armada. But I could be completely incorrect.