Reports out of Fort Myers are that Scott Baker threw without problems today, but not at full speed. He will do a bullpen Monday. If that goes well, he will be ready for his next start on Thursday March 22nd. He will only have missed one start with two weeks to go in spring training. If there are no further setbacks, he will very likely be ready to pitch the home opener on April 9th.
If he does have a setback, there is still some wiggle room for him to get in three starts before spring training ends. But at that point it becomes more likely the Twins will use the day off after the home opener to skip his start. His first start wouldn't come until April 15th*. In any case, unless there is a serious setback, it does not look like the Twins are going to have to find someone to replace him in the rotation.
*UPDATE: To clarify that, April 15th is the first date when the Twins will need a 5th starter. Since everyone in the rotation will have had a day off, Baker could start earlier than the 15th if he is ready and they want to position him higher in the rotation.