Perhaps counterintuitively, this is even moreso the case the more successful a YC company becomes. There's little to nothing that YC can do to help Dropbox, but there's way more that YC can do to help a struggling 5 person company get off the ground.
Working at a successful YC startup can only help your chances.
We just don't have much interaction with the partners anymore since their focus is better spent on the recent batch rather than helping 4 year old companies.
I think you should go ahead and tell your founders about your aspirations. They may very well be supportive; I've definitely read that many YC founders encourage their employees to do their own startups. Telling them will give you and them a chance to work out a plan for what you should get done before you start applying to YC or other accelerators in earnest.
And if they're not supportive, well, maybe they weren't so deserving of your consideration as you thought. I find this hard to imagine, though. It's not like you're quitting outright.
I don't know about the specific case, but a 4-year old startup should have enough cash to spend a little in a small seed capital.