[1]: https://upload.wikimedia.org/wikipedia/commons/d/d6/US_Navy_...
[1]: https://upload.wikimedia.org/wikipedia/commons/d/d6/US_Navy_...
Considering the Challenger's encounter with the A380's wake, it took 1-2 minutes for the Challenger to hit the wake, so the wake probably had 1-3 minutes to make the 1000-foot descent. That very roughly fits the expected "several hundred feet per minute" descent rate.
Considering the case of refueling, the wake's motion downward is much slower than the aircrafts' horizontal motion, so it wouldn't have descended much by the time it's left behind entirely.
[1] Available for free at https://www.faa.gov/regulations_policies/handbooks_manuals/a...
https://aviation.stackexchange.com/questions/9572/how-do-air...
http://cfile29.uf.tistory.com/image/145D430D4CFE23D50A5BD0
being close is relatively safe from wortexes - there still is some other turbulence to consider, but the standard turbulent flow caused by drag is chaotic so it'll shake you but will 'even out'