Lol, no way! The N-Series will have a 1:1 (720x720) resolution, which means a 3.8" display would be too wide, especially with a keyboard attached at the bottom.
Chances we'll see a 3.0 or 3.1" screen are pretty good. Maybe even 3.2", but I highly doubt RIM can get more out of a classic, Bold styled device. Keyboard and screen size are limited to the overall dimensions of the phone.
You could only bet on a Torch like slider. There screens with 3.6" to maybe even 4" would be quite possible. Dell already has shown you can produce a decent 4.1" slider with acceptable dimensions.
Laws of physics (overall phone size) simply limit RIM to do any miracles. So if you really want. To have way above 3.5" displays, you'll either need to go full-touch or hope for a slider. But a Bold with such a massive display simply won't work.