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.

You'd need to turn it all the way over, which is likely to upset the passengers.

This has actually been tried as a last resort. It didn't end well unfortunately. https://en.m.wikipedia.org/wiki/Alaska_Airlines_Flight_261?w...

The reason for the nose down is to prevent a stall.

Rolling the plane in stall conditions can cause a spin, which is very, very bad. A spin is an aggravated stall which is harder to recover and puts a lot of stress on the airframe.

While almost all planes can safely recover from stalls given enough altitude and pilots are trained for it, spins are normally limited to aerobatics.