No, it's not just a convention. 'main' is defined as the execution entrypoint in at least the C11 [0], C90 [1] standards. Both have both these forms defined:
int main(void) {}
int main(int argc, char* argv[]) {}
You don't have to follow that convention, but then it becomes implementation-defined behaviour.
C without libc can still expect to have a main. One doesn't imply the other. It's just without a main, you also have to manually link to _start as well.
In fact, main() is just a convention of libc. You can have C without libc. (Such as when writing a kernel!)
Now, attempting to link a standalone executable without a '_start' symbol, on the other hand...