Yes and No.
It depends on which version of C++, you're using.
- C++98 and C++03 do not support explicittype conversion operators
- But C++11 does.
Example,
struct A
{
    //implicit conversion to int
    operator int() { return 100; }
    //explicit conversion to std::string
    explicit operator std::string() { return "explicit"; } 
};
int main() 
{
   A a;
   int i = a;  //ok - implicit conversion 
   std::string s = a; //error - requires explicit conversion 
}
Compile it with g++ -std=c++0x, you will get this error:
prog.cpp:13:20: error: conversion from 'A' to non-scalar type 'std::string' requested
Online demo : http://ideone.com/DJut1
But as soon as you write:
std::string s = static_cast<std::string>(a); //ok - explicit conversion 
The error goes away : http://ideone.com/LhuFd
BTW, in C++11, the explicit conversion operator is referred to as "contextual conversion operator" if it converts to boolean. Also, if you want to know more about implicit and explicit conversions, read this topic: