Yes. An injured player doesn't need to go onto the Disabled List, and they frequently don't, especially for a minor injury. The Disabled List is a device set aside so that players who cannot play can be kept on the team's roster for 15 or 60 days without using up a roster spot. In other words, if a team called the Bulldogs had a center fielder named Bob Jones who had to miss 15 days, they could put him on the 15-Day Disabled List, which would allow them to call up a minor league player to use his roster spot, with no penalty. If he is not put on the DL, then he can start playing again at any time, but his roster spot cannot be filled by anyone else.