If electrons move through higher voltage, would a neutral conductive object get charged positively if I were to connect it to only the positive terminal of a battery?
As in, would the electrons would move to the higher potential, leaving the object charged positively?
Almost zero charging would happen. Batteries create a potential difference between the terminals, not an absolute potential.
If we touch the positive terminal to a large object, the positive terminal and the object will move to the same potential. But this will probably happen by the battery changing potential, not by the object changing.
Then the negative terminal will be $V$ volts below the object and the positive terminal. And because both are probably poor capacitors, this will only take the movement of a very tiny amount of charge.
say you made the conductive object neutral by touching it to earth, and th negative pol of your batterie ist connected to earth, then your object would get charge touching only the positive end of you batterie. How else can you be sure your object is neutral. or the pol of your batterie is positiv? Positiv is always compared to something .
