Incorporating lawn rakings into soil?

Hey r/gardening. Here in Manitoba, Canada the last risk of frost is late in May (in a normal year, no idea about this year). But I got out and raked out some dead grass out of my lawn. Rather than bag it, I tossed it on top of a bare garden bed. My immediate thought is that it would reduce erosion from wind.

Is it OK for me to just dig it into the soil? What would the benefits and harm of that be?