You can however, check YSE (my blast yesterday increased by 300+ links) or google your site name in quotes (no www or http://) and you will literally see the links pile in (100+ per hour for me yesterday, YMMV).
Additionally, you could use majesticseo.com or ahrefs.com to watch your backlinks pile up in almost real time, check this recent test blast (trying to see how an aged site with hardly any links and no updating in 2+ years handles it).

