No. Now a substantial part of the lift no longer points up because you use it for turning instead. That's why when you turn you have to increase lift (i.e. you

No. Now a substantial part of the lift no longer points up because you use it for turning instead. That's why when you turn you have to increase lift (i.e. you pull back a bit, or adjust trim if it's a shallow turn that takes a while to complete) or the nose drops, to compensate for the loss of lift by not using all of it to remain at the original altitude. Remember that unless you have negative or zero g you always have positive lift even with a nose pointed down, so taking away some of it won't help you, you'll just help gravity. You could slow down (forward speed) - if you can, that is. Banking won't help your descend rate all else remaining equal.