When you rebuild an index the database engine creates what is called an "intermediate sort result." These intermediate results are like chunks that are combined to become your index and creating these chunks requires space. If it can the database engine will actually sort the index in memory; but if not it will store the intermediate results in the destination file group.
Using the SORT_IN_TEMPDB option asks SQL Server to store these intermediate results in TempDb instead of rebuilding them in the source database. When the TempDb resides on a different disk to the source database this can help the performance of the rebuild task and can reduce the performance impact on your database.
A requirement of rebuilding indexes is that you must have sufficient space (wherever you decide to build the index) to hold the largest index in your database: this in your example is 25GB. Which, if you use TempDb you should quite easily have.
As to whether your source database will grow, well I wouldn't rule it out but it won't grow anywhere near to what it would if you rebuilt the indexes within it. If you are concerned about this fact then take a copy of the database and put it in a test environment and try it out - it is the only way to really know for sure.
I hope this helps you.