Yes, but ONLY in full-season leagues - there are no injuries or suspensions in the exhibition season games. Also note that goalies cannot be injured, only skaters can. Goalies can fatigue severely, but will not get injured.
If a player is injured in the game, it will be highlighted in RED in the play by play. Guys can go down for a period and come right back or be out for one or more games.
Players can also be ejected for poor conduct during a game. Upon completion of the game, the league will review all ejections and determine of a suspension is warranted. If they play is suspended for any games, you will receive a notice in your SiteMail box telling you of the suspension.
If a player is injured bad enough where he cannot return, or he is suspended for a number of games, the status will be displayed in "Players Out" option on the top menu bar on most SimLeague Hockey pages. In this window, you will see the injury or suspension description, the numbers of games he will miss, and his return date. Until he is cleared to return to action, the player will be unavailable to play.
Injuries are based on how many total minutes the player played in real life. If you draft players that played lots of games in real life, the odds of them getting injured are very small and if they do get injured, it won't be for very long. If you draft players that only played limited games then they will suffer more injuries and for longer periods of time.
Suspensions are based on the penalty minutes (PIM) the player had in real life. Players with higher PIM averages per game are more likely to be suspended in the SimLeagues.
There is a limit on how many players you can have out at the same time. The default for open leagues is 8, however this number can be adjusted for theme leagues.