I don't use the thread cutter when machine quilting. If I understand your questions:
If you tie the end of the quilting by using very small stitches (0) and moving the stich back and forth or round a bit
then you don't need to bring the bobbin thread up. You will only need to bring bobbin thread up if you intend to bury the tails in the batting.
When I am quilting a straight line and come to the end, I will usuall just hit the back stich and let it go a couple stitches, remove the piece with a long tail and no bringing up is necessary. Now if you are quilting to the edge and going to attach binding, I usually forget to do the very small stitches or back stitch. In these cases I may go back and put a dab of Fray Chek on the ends to make sure they stay in and will be covered by the binding.
Now. Now if I am quilting a long line within the quilt I will always leave a long tail and bury the threads. I don't worry about pulling the bobbin thread up but will do that when I get ready to bury the ends. In these cases I don't do a back stitch or the tie stitch on the machine as double stitching will usually be noticed (by me) and probably leave a darker dot on the quilt.
Hope this answers some of your questions.
I just feel that I have better control to use scissors to cut the threads. Also I have read and heard that it is not good idea to use the thread cutter when machine quilting as it doesn't leave enough tail to bury or tie off.
Also, on some of my machines when using the tie tack stitch it will put a knot on the top and I usually accidently cut this off when I am trimming the end thread and loose the secure end of the quilting.
I never recommend these features in my classes.