YES, they care. Most schools I applied to will not take a grad-school drop-out within one year of dropping out, if at all. If you don't want to do this MA program, don't matriculate.
Also, my acceptances typically were contingent on completing all degree programs in which I was currently enrolled.
My grad school automatically assigns an expected graduation date of 3 years after matriculation (even though my program was 3 semesters), and my pre-med advisor considered this so important that she made me get the registrar's office to change the date to my actual expected graduation (a year earlier) so that it wouldn't screw up my applications. I'm sure there are exceptions, but she said that no one would take me in the middle of a grad program. One school required that I furnish proof (letter from my advisor) that I would finish by this summer before they even considered me for an interview.