I always keep one or 2 on the kick drum, I keep 2 in a holder on the hats. I've never practiced it but gotten better at it over the years.
The music I play is FAST, so when I drop a stick it's already too late. I've had to figure it out for a few bars even though it's only a few seconds.
The good thing is is I don't drop sticks often these days. I practice technique and staying relaxed. that really helps. along with Making sure your not hitting rims if your using a house kit or catching it on a rim during a fill etc.
Rather than practice picking up a stick, practice keeping the beat with one hand. practice with the other hand solo. So sure, you could practice dropping a stick, but ride it out for a few bars then find a spot to grab it. The key is to not loose the time and groove.