We run ad campaigns to attract potential customers to our website. Sometimes customers click, but don't make contact. Is it acceptable to reach out to these customers, based on the public info available from their IP?
Creepy. And kind of presumptuous.
There's nothing technically or legally(?) wrong about this, but the reaction is probably going to be uncomfortable at best, to even hostile.
If you really want to do this, I'd suggest acting as if it were a cold call. You get the benefit of using the information gained from your logs, without coming right out and saying you basically stalked them. I'll leave it as an exercise for you to justify the cold call itself, but presumably these are people within a given industry or something, such that there'd be a reasonable way for you to find out who they are by other means.
No. First, I don't know how you are going to be able to find this customer based on their IP. Even a static IP (that doesn't change) may be used by multiple computers and even any single computer may be used by multiple users. You have no way of knowing who the potential customer is or how to contact them based on their IP.
But secondly, even if you had a way to contact them, no it would not be considered acceptable. If a potential customer clicks and goes away, there's nothing you can do. I recommend looking into ways to attract them further before they leave, such as offering chat services, collecting an email address, tracking pages with analytics to see what kinds of pages have lower bounce rates and try to determine why, or other similar possibilities.