Technically, yes: any sensor data can be used to construct a map. However, if you want an accurate map, you need accurate sensors. If you read Admin's tutorials on sonar and IR sensors, you'll notice that the sonar works better as a "bump" sensor, because its detection area is a large bubble, whereas the Sharp IR sensor is more of a line. Using IR sensors, you can get a more accurate map reading. However, this is all theoretical, I've seen SLAM algorithms (algorithms that create a map and figure out where they are at the same time) that use only two sonar sensors.
If your trying something simpler, such as using a pre-created map of a room, house etc, you don't have to update the map very much, if at all. You could implement what is called 3-point turning (I think that's what it's called): if an obstacle is detected, the robot would go around it and return to its original path like the obstacle never existed. So, you could create a general map and send the robot to a location on that map. If an obstacle is detected that the map didn't show as a blocked cell, just go around it and continue on its original path, don't worry about updating the map. This type of obstacle avoidance can be done with a single sonar sensor on a servo, so it's the easiest way.
I agree with pomprocker on getting encoders, they are a must-have for path finding and mapping projects.
