Yes. You can either select Saturday or Monday as the start. Either way it'll just cost you the one day ($6) as the weekends on the edge of the stay are free.

You can do this even if you're arriving on Friday before 3pm - just pay for Friday as if it was a normal stay (ie, pay $2 at the ticket machine - just remember to take note of your space number), and then use the airport parking for Monday only (or Sat-Mon).

BART parking is free from 3pm Friday until 4am Monday, and more importantly, the 24 hour maximum rule does NOT apply during that period, so you only need to worry about the periods before/after those times.