I just went through that process with a King size scrappy quilt. Despite having trimmed the blocks before adding them to the quilt, by the time I was done with it and the borders there were lots and lots of loose threads.
I laid the quilt out on the dining table where I could do 1/2 the width at a time (and perhaps 1/5 the length). With a small thread snip in my right hand, and tape wrapped around my left fingers, I would snip then stick them to the tape.
A long tedious process, but I was sending the top to an LA. If I was quilting it myself on my longarm I wouldnt have bothered because I float my tops and I could have flipped it to remove any offending theads when quilting.
For me, it was worth it. I know how discusted I would have been if I saw threads showing through after spening so much time on the quilt. Better safe than sorry.