First of all, the “very conductive material” will form a conductive path only if it isn’t insulated, i.e. if it is grounded or connected to a different phase.
To answer your actual question, current WILL flow through your body (alongside a lot more current flowing through your pinky), but less than that in the case where your pinky isn’t touching a grounded conductor—by about 50%. Let me explain.
If your pinky isn’t touching anything, most of the line voltage will gradually drop across your body, or maybe across whatever sits between you and ground (perhaps insulated shoes). That means your hand (let’s say your wrist, specifically) will roughly be at the line voltage, and the current through your body is the line voltage divided by the impedance (essentially resistance in AC circuits) of your body, plus the impedance of your soles, etc.
If your pinky IS touching a grounded conductor, the entire line voltage drops across the short path between the tip of your index finger and the tip of your pinky. The voltage at your wrist is roughly the same as the voltage halfway across this path, which is half of the line voltage. The voltage across your body (i.e. between your wrist and ground) is then roughly half of what it would be if your pinky weren’t grounded, so the current through your body is roughly halved compared to that case.
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