It wouldn't matter, if you have a protagonist that you wouldn't give a rats-ass about. But if you have a character driven storyline, then you would definitely like to know about his/her past and why he/she are the way they are and do the things they do. It helps create a different level of immersion in a character's storyline. For example, I loved Kane & Lynch: Dead Men. I would like a prequel explaining Kane's history with The7 and Lynch's side of the story too. None of these are properly explored in the first game, nor the second one.
If I would have played Devil May Cry, without playing DMC3, I would have had no idea who Dante was (apart from being a Demon Hunter), who was Nelo Angelo, the essence of Eva's amulet, Why was Dante's shop called 'Devil May Cry' etc. This is where Capcom gets brownie points for explaining, exploring and giving a new dimension to Dante's character by giving us Devil May Cry 3.
This is exactly the reason why I found Ezio to be a more like-able character compared to Altair. In the first game, right from the very first cut-scene, we were just thrown in as Altair and led onto Assassinate one person after another. Whereas, the second game (literally) gave birth to Ezio and led the player to take over his role right from his birth. Every detail of his life was depicted and hence people actually grew to like his character, both as; A witty and charming person & as a trained Assassin. See what happened here. There was a connection established with the character. His missions were crafted, in accordance with the way the events of his life unfolded. It was like watching a beautiful movie. This is why the second game was praised and Ubisoft had got everything right in this game, which wasn't present in the first game. Of course, I'm taking into account the re-vamped gameplay as well.