Yes, *this is always an lvalue, no matter how a member function is called, so if you want the compiler to treat it as an rvalue, you need to use std::move or equivalent. It has to be, considering this class:
struct A {
void gun() &; // leaves object usable
void gun() &&; // makes object unusable
void fun() && {
gun();
gun();
}
};
Making *this an rvalue would suggest that fun‘s first call to gun can leave the object unusable. The second call would then fail, possibly badly. This is not something that should happen implicitly.
This is the same reason why inside void f(T&& t), t is an lvalue. In that respect, *this is no different from any reference function parameter.