No, the ISO C standard states that a main function is only required for a hosted environment (such as one with an underlying OS).
For a freestanding environment like an embedded system (or an operating system itself), it’s implementation defined. From C99 5.1.2:
Two execution environments are defined: freestanding and hosted. In both cases, program startup occurs when a designated C function is called by the execution environment.
In a freestanding environment (in which C program execution may take place without any benefit of an operating system), the name and type of the function called at program startup are implementation-defined.
As to how Linux itself starts, the start point for the Linux kernel is start_kernel though, for a more complete picture of the entire boot process, you should start here.