I am going to speculate that this will be an issue and that it will become painstakingly evident very soon. Firstly, the shortened season will increase the intensity of play among all players because each game has become more important in determining whether or not a team makes the playoffs. Aside from that, there is now a much more powerful incentive to target star players and try and take them out of the game or a stretch of games. Therefore the rats in the league should be running wild.
IMO the senators won't be in a good position for this. We have a handful of injury prone players (Lattendresse, Michalek, Regin and to a lesser extent Spezza and Alfie) that are very likely to miss a significant amount of time due to injuries from the increased physical play.
On top of that, we aren't really in a great position because the strength of our depth comes from our prospects. Those prospects are too new to the NHL to carry the load offensively. So we will likely go on a losing streak if we lose a few of Karlsson, Spezza, Alfie and Michalek to injuries for any length of time. Hell even if those players can be taken off their game from the lack of time and space could severely negatively impact the success of the team this season.