Hammer Ons, slides + simultaneous note picked in tab?

Hi, long time lurker, infrequent poster. I'm a new banjo player (started back in August) and I had a question about something I've noticed a fair amount in tabs I'm learning. I've often seen either a slide or a hammer on where an additional identical note is in the tab to be picked on a different string (or at least that's how I'm reading it) such as:

----0----------------------
--2^3----------------------
--| |----------------------
--|_|----------------------
---------------------------
    H 

I'm assuming the tab wants me to play the same note on the 1st string in the above example, while I hammer on the 3rd fret at the 2nd string. It just seems strange since it's the same note. Is this just to get more volume out of a hammer-on or slide by playing the same note elsewhere or is there something I'm missing here that isn't spelled out in tab?

Thanks!