No, if it was all fluid; but too much air in fluid would. You might get shop to just listen to sound/symptom @ this point. Is the wailing/siren sound worse as you turn steering wheel w/engine running? Try in P or doing figure 8's in a parking lot. Sounds like the tech was too rushed to properly get air out of pow. steering system after he filled it; air bubbles expanded w/pressure & heat
created by pow.steering system operation, increasing air/fluid volume. Anyway, get fluid level where it belongs. You want to get air out of system. Let engine idle w/cap off p/s resevoir. Have a cup of coffee and "hang out". Periodically add fluid if nec. (Take note of "hot' and "cold" lines on p/s dipstick.) After 7-8 minutes turn steering wheel lock to lock and see if your sound is gone. If no, go do a lot of fig
8's, come back, and refill, if nec. If symptoms still there, check/add fluid. Now you could jack up front of car if poss; w/tires off ground turn steering wheel lock to lock for maybe a minute; (be safe); then check/add fluid. Go for 1 last fig 8 ride, and check/add fluid. If sound is still related to turning of steering wheel I think damage was done to p/s pump and/or steering gear by the tech not getting air out of
system. If sound seems totally unrelated to turning of steering wheel, it's something unrelated. Or, you could have shop do the work of getting the air out of system- I'm just trying to give you the big picture. Good luck.