If you want to know when a given backlink is indexed by Google there is a very simple way to do this
Check the Google cache date on the page. Check it every day till it changes then you will know how often Google revisits that page. Then you will know how long that page takes to update and that is also the how long it will take to index that backlink.
Google pays more attention to homepages and category pages ( mostly for non-commercial sites - aka blogs ).
So it will vary from site to site. From a few days to a few months...