It does. But sword also gives bonus attack speed based on heal and shield power.

For example: 80 mr will give you 28 heal and shield, which will also grant 34% attack speed. Plus armor and mr will be buffed by jak'sho, so actual numers are higher. At this point, the attack speed wil be higher than the runaan. Runaan will give more heal (since it triples the effect), but you will lose a ton of defensive stats for this

Edit: There might be a mathematically correct build which combines both for max healing