Yes.
But the skill level can/will determine how much a difference there may/will be. At a minimum, a superior camera will increase the ease of capturing the exceptional image as well as increase the consistency (keeper percentage). (Ease of capture helps consistency and keeper rate.)
I've owned cameras that were atrociously poor (Argus C3) in terms of ergonomics and functionality, and cameras that were basic on controls and had average ergonomics (Nikon FM, for example), and famous classic cameras (Nikon F Photomic FTN and F2A and F2A-SB) and Nikon F3, Nikon FE-2, and many (12 different models) of digital SLR cameras from awful (Fuji S1 Pro), to good, Fuji S2 Pro, Canon 20D,the Canon 5D, to extremely good in the Nikon D2x,to the very finest camera of its era, the Nikon D3x...and am currently on a pair of Nikons the D610 and the D800...I can tell you that a camera with a small, crappy viewfinder like the Nikon D70 is a poor rig compared to the D3x or the D800...the high-end, $3,499 to $7995 cameras truly are _better shooters_ than the low-cost models.
A superior camera is simply easier to shoot with.It shoots quickly. it has great controls. It has all the features you will ever need. As Gary mentions, a superior camera, after one familiarizes himself with it, leads to easy shooting, and lots of well-captured images, on a consistent basis. Once you own a top-level camera for a while, you realize that almost invariably, any mistakes or errors are your very own fault, and you lose the ability to blame the equipment.
Does the camera model really matter? At times, YES; for example, the low-end Nikons do not allow FP Synch or full remote flash capabilities, so, an entire class of flash photography is not within the scope of the $488-$699 models; the cameras actually LACK advanced features. The same thing exists with some other features, like buffer depth, or speed of sequential shooting, or low-light autofocus capability, and so on. At times (and not a "lot" of times), yes, the camera model can be an issue. However, as I see it, for the majority of uses, many models of cameras will provide adequate performance. However, there have been a number of cameras I have owned that were not all that good at focusing in tricky situations, or with consumer-type lenses with slow maximum aperture values.
The MOST-important difference I will say is to look at the viewfinder' size, brightness, and clarity, and how well it interacts with your eyeglasses. Same with rear-LCD viewing and/or flippy screens. To me, the superior viewfinder camera is the one I WANT to use....this is where the low-level d-slr cameras have small, "squinty" viewfinders, which for me, hinder my shooting. The better the viewfinder, the easier the camera is to shoot, in my 40-plus years' worth of experience.