Yes, and this is the correct way of the rules.
Look at other cards with draw bonus and you will understand how it works (without bonus = normal draw and with bonus = you add card(s) to draw).
De rien
You get the "effect" regardless of whether you pay with the right cards for a bonus. The effect is draw 1 card, and you always get that 1 card when you play the owl.
If you pay with the correct suits to qualify for the bonus, then you also get the bonus - that's draw 2 cards. But a bonus doesn't cancel out the effect - you _always_ get the effect. So 2 cards for bonus, and 1 card for effect.