Dear Miss Snark:
Could we hear your comments about the likelihood of a POD book being picked up by a commercial publishing house? Do POD publishers share in any royalties if the book is picked up? Would an agent in his/her right mind take on a POD book in an attempt to sell it commercially? Have you ever received a POD book in the mail for representation? If so, what did you do with it?
Let's start with a basic review of terms. POD is a way to print books. (Yes I get lazy and misuse it too). What you're asking is if a writer self publishes a book using POD technology, OR "sells" his/her book to one of the vanity publishers that uses POD, is there a chance it will get "picked up".
Picked up is TV or sports jargon. In publishing, we talk about selling rights. Your question is, I think: If I publish with a company like Lulu.com, or iUniverse, or on my own with a small print run, will a big house be interested in acquiring the rights.
Answer: probably not. Totally not if you write a novel. Less totally but still not much if you write non fiction, and totally totally not if you write poems or family cookbooks or family genealogy. Now before you find the exception to this and wave it in my font howling "you're WRONG!!", remember there are always one or two exceptions to the 50,000 books published that way and if you want to spend time and money trying to be 1:50K, go for it.
IF by some stroke of marketing genius you do end up selling rights to the book to someone else, whether the first publisher shares in any of the money is dependent on the contract. Whether you are able to sell the rights is also a matter of the contract language. If the first publisher own the rights, you can't sell them till you get them back.
I don't know of many agents who are keen on selling previously published work unless something else sweetens the deal.
People have sent me previously published books without querying. I throw them away. The library won't take them, and I'm not schlepping them to Housing Works on the train.