I am also in MA.
Once your FMLA has expired, your employer has no further obligation to return you to work. While they MAY continue your leave (without FMLA protections) they are not REQUIRED to.
Whether your specific injury is considered a "disability" depends on how you are using the term and what you are looking for the definition to do for you. It may well still be a disability for purposes of your STD benefits (if any). However, just having a "disability" does not mean that you're automatically entitled to additional protected leave time. IF your condition qualifies for protection under the ADA, a SHORT extension of your leave might be considered a reasonable accommodation, but not an unlimited extension or even a long extension. Even under the ADA, you are still going to have to be able to return to work and perform the essential duties of your position. If you cannot, your employer does not need to continue your employment.
The bottom line is, if you are looking for a guarantee that you can take as much time as it takes for your thumb to heal and still be guaranteed your job back at the end, sorry but I cannot give you that guarantee.
I do have one question, though. Is this considered a work-related injury? If so, MA has a unique law that MAY provide you with a bit more protection that you would receive in any other state or in MA with a non-work-related injury.