Yes. All schools that are members of MLS are welcome to join the MLS instance of OverDrive.
If you have already purchased content, you will need to consider what you want to do with your current OverDrive collection. It may be possible to merge your school (or district)'s collection with the MLS collection or you may want to join the MLS Overdrive instance and keep your existing collection separate.
If your school/district is on the free Sora platform, you can join the MLS program to get access to even more titles!