The quality of your images will vastly improve, but your photography won't get any better (obviously

).
Comparing a 350d (I have one) to a 40d (I regularly play with them at work), the difference is substantial.
The 40d's screen is much bigger, which makes a huge difference.
There are 2 wheels to change settings, rather than one, which makes a huge difference.
The settings screen is on the top, which makes a huge difference (recurring theme here

).
The noise control is far better, meaning shooting at higher ISO's, theres a lot less noise.
There are more megapixels, meaning that cropping is less intrusive.
Ergonomically, the 40d feels a lot nicer (not everyones taste, mind).
There are more buttons to try and figure out what they do (again, not everyone's taste).
There is a joystick to navigate the menus, making a big difference.
It has live view, which makes composing difficult-to-see-through-the-viewfinder shots easier.
It has more frames per second, meaning you could capture that all important shot.
There are various other things, but I can't think of them off the top of the head.
In a nutshell, YES! UPGRADE!