This is a question I get asked all the time and there are so many factors to take into consideration before the question can be answered properly.
There are many types of backlinks and they are not all made equal. For example, if you some how manged to publish a blog post with a link to your site on the BBC then this page is going to be indexed pretty much immediately because Google is constantly spidering the whole site for new content. If you create a blog post on a new domain or some obscure Web 2.0 site then you are looking at a much longer time frame. Also, if you are using automated software with poorly spun content then there is a possibility that it will never be indexed.
So when should I use a Backlink Indexer? Well, if you ARE using automated tools to build your backlinks then you really need a helping hand to get those backlinks at least ‘crawled’ by the Search Engines. If you are not building tiered backlinks (and I recommend that you do) then it is difficult for these new backlinks to get spidered. Using a backlink indexer will at least get Google to crawl the link and then it is up to Google whether or not to index the content. This why it is imperative that you at least use good quality spun content or even better, unique content to increase your chances.