Does the under-eye filler procedure take a long time?

It’s bad enough having dark circles under my eyes, but since my tear troughs are deeply sunken, I hear people say I look haggard all the time, even though I’m not tired.

Since concealer doesn't cover it, I am seriously considering fillers that only add a subtle amount of volume.

I want to squeeze in a quick visit, but excluding the waiting time at the hospital, how long will the total filler procedure take, purely from applying the anesthetic ointment to getting the injection? I heard that the doctor administers the injection delicately while shaping the area, and since it is a very thorough process, I am worried it won't finish quickly.

I'm also wondering if the results aren't very noticeable even if I return to work immediately after the procedure, as it finishes quickly. Please share some tips from those with experience on whether getting fillers during a weekday afternoon break will interfere with my afternoon schedule!