OK, let me cut it down to you.
NO!
Why? Because Graphics, contrary to belief, doesn't affect the budget that could spent in other areas as much as people like to believe. It has to do with planning what the developers and team leads had in mind from the beginning. Believe it or not, many times a studio will cut corners in a graphical department, not the programming...what a surprise many people didn't know.
I mean how many games do you know that look like utter crap and don't stand two sticks in plywood in gameplay or story? How many games do you know that experimented with new ideas and had either good graphics or were, in terms of design pleasing?
In the world, in a year we have between 500-800 games being released, which aren't simply flash games, but actual budget games, and surprise, surprise, I mostly see game with great idea, crappy graphics, and even worse execution of mechanics.
People tout this flag of graphics, citing it as the reason games blew goats and money being spent there. Most animations are mo-capped and cleaned up in a studio, and more and more studios use small scale software which bridges this problem but automatically cleaning as much crap as possible, only giving what the animator can use under 30 frames per second.
Shaders? A few years ago, having skin like effects for you characters was coded by hand and a notepad with math formulas, now we have visual editor which are like networks which allows even dummies like me to create human skin in a matter of hours, and if I want to get more complicated, in matter of days with immediate feedback as opposed to weeks of testing.
Modeling characters and environments (things such as damage and tear wear effects) are done dynamically through pre-created computation, such as the software reading the hard edges of a gun and apply a 'dirt' map to those area instead of having the artist manually go in and do it by hand and achieving a fake look since it's not random and 'correct' enough.
So yeah, in anything, graphics aren't having any money invested them on ANY scale people like to think. You should watch Extra Credits video about Graphics vs. Aesthetics for that is a more correct debate.
