Yes, spell-like abilities DO count as having the required spell or spell level in question.
BUT, if you can only cast a 2nd level spell-like ability, and the requirement asks for a 1st level spell, you're out of luck.
So, a Gnome or a Drow noble can take Arcane Archer, without having any arcane caster level, while an Aasimar or a Tiefling can't.