Looking at their
list of vendors, if you look down at "Alajuela" you will see "Aeropuerto Internacional Juan Santa MarÃ*a", "Lunes a Domingo 5:00am - 10:00 pm." As long as you arrive within those hours, you should have a good chance. OTOH, it is Central America.
One thing you might want to consider. ICE seems really big into
"homologation" of handsets. You might also want to make sure that you take a handset you can show them that will
pass muster. I have no experience to say that they would reject you if you don't produce a handset they say is OK but it would be a pain to get there and have them say "no" because of that.