Does it make sense to Learn C for an IT degree? Even though my aim is to be WEB developer? [on hold]

I want to go to college and earn a degree that IT employers will recognize. I am considering Full Sail's Web Design & Development program because its exactly what I want to do as a developer FRONT END that is.

I just don't have the money to pay the difference of with Financial Aid.

So...

I figure I'll go to this community college at no cost to me to obtain my degree a either Computer Programming & Analysis OR Computer Information Systems, get a real world job programming, and then go back when I am able to pay out of pocket.

--- My dilemma

Both programs are focused on writing C programming code. A language I am not very familiar with. I have been programing for about a year or so now, mostly front end stuff recently picked up angular, node, and express js.

--- bottom line

What do you think? Will learning C programming REALLy help me be a better Web developer???

is it worth going to school... for what I will become?

and what advice have you for someone with my experience?

also whats the coolest thing ever programmed in C? (for motivation)