Yes! I have seen that same excuse used many times with success in the past. This is especially true if you are able to articulate why only you can provide the level of care necessary for your disabled parents.
For example, you may be the only reasonable person to provide this care if there is special training that you have had on how to care for their specific condition, how to administer medications, or any other special knowledge you have that cannot be easily taken over by someone else.
Consider all the reasons why it might be detrimental to the care of your parents if someone else, who was not familiar with their specialized care requirements, took over while you were serving on the jury. Articulate this to the judge and you have a very high likelihood of being excused.
Just be prepared for when the judge asks you, "Who is caring for them now while you are in court today?" and the follow up question of "Why can't they care for your parents while you are serving as a juror?"