By the sounds of it your not the one collecting the email address. Your affiliate is but is offering that information to you.

I would be very sketchy on marketing to them addresses unless it was you collecting them or a coregistration deal. Check the affiliates privacy policy and email them and ask if its they allow you to follow up directly.

I personally would not use them unless the affiliate gave the ok and it was ok according to there privacy policy

Right, that's exactly what's going on. I did not collect the emails.
So basically, as much as I would like to use them, I will stay away.

The only way of building a list and doing email marketing is with Double Opt In.

The information you got is the same as anyone selling email lists but you got them for free.

This is incorrect.

First, we need to clarify some information. The way I'm reading this, you are the affiliate and the company whose affiliate you are was paying you when someone completed and action. If a visitor enters their contact information without completing the payable action, you are given the option of having the vendor send a reminder email after a certain amount of time. Correct?

Or is the vendor giving you the email and a pre-written template email to send on your own?

It makes a difference.

If the email is going out from the vendor's account in the vendor's name, you should be okay with a single follow-up about the offer they initially volunteered their information for.

If the vendor is asking you to send an email from your own account, that's different. You have no previous relationship with the visitor - they gave their contact information to the vendor, not to you. So unless the vendor's privacy policy allows for contact by affiliates (and it might well), the vendor is asking you to spam on their behalf.

Technically, confirmed opt-in (aka 'double opt-in') is not required. Many third party services do require it to discourage spammers from using their service. It's the same reason many services won't allow you to import outside lists.

That said, those addresses don't belong to you. Those people opted in to receive information about a specific offer from a specific vendor, not to land on your list and get offers from strangers.

Without reviewing the specific privacy policy, TOS and affiliate agreement for exceptions, it sounds like you can't legitimately do anything with those addresses.

Sorry...

Not a good idea if you send email to the list that is not opt-in. Because this will not only increase the spam rate of your email campaign, but also harms your sending reputation if you are doing in-house email marketing.

Thanks for all the replies everyone. After reading the replies I realize now that it was silly to ask. I knew the answer just needed someone to say it for me to realize it I guess. I wouldn't want some stranger using my address in this method and I won't use these ones.