There was an article in a computer magazine recently about this. There is only one printer on the market currently that can print photos with the longevity of those done by a developer. Its an Epson and retails for around $900. The estimated life of these photos is something like 75 years.
All other printers when tested produced results that can last for anywhere from 3 to 26 years before losing quality. So the answer to that question is, for the most part, no...they won't last as long. I don't really know what you mean about photo quality printer ink. Some printers print in what they call "photo quality" but this does not have a bearing on longevity, just how the photo looks when printed. And most printers will only accept printer ink cartridges designed for that particular printer brand and model.
As far as being safe for scrapbooks...if the paper you are using to print is acid free, lignin free and buffered it is completely safe. If there is lignin in the paper it will eventually yellow. If the paper is not buffered it can eventually become acidic. The biggest issue, besides keeping the digital prints from being ruined, is keeping those traditional photos from being damaged by migrating acid or lignin that comes into contact with them. If you back anything questionable with paper that meets the above criteria and make sure you don't let photos come into direct contact with anything questionable the photos should be fine.
Hope that helps,
Lesley