TL;DR: no, things don't work that way.
To create the impression of gravity by spinning, you need to be inside the spinning object. Mass is nearly irrelevant to this. The characteristics that matter are spin speed and distance from the center.
If you are standing on the spinning object, the spin pushes you away from the object. This makes us slightly lighter on the Earth. But overall, the gravity effect (unrelated to spin) is greater than the push away from the surface. On a small, fast-spinning object, you could actually be pushed off by spin.
Once you lose contact with the spinning object or if you never were in contact with it, the spin becomes irrelevant. You now have a straight line velocity and an acceleration towards the mass. If the velocity is high enough (called escape velocity), you will eventually move far enough away that the acceleration by gravity becomes negligible.
You cannot escape spin effects by spinning an object that you are not touching to create a gravity-like effect. It won't do anything. You need to be spinning with the object for the gravity-like effect.
What's actually happening is that the spin gives you a straight line velocity tangential to the circle of the spin. But because there is a centripetal force, i.e. a force pushing you towards the center, your direction is constantly changing such that you follow a circle and feel like you are being pressed down. But you are actually traveling out and being pushed up.
You have a similar effect in a fast rising elevator. You feel like you are being pressed towards the floor. But what is actually happening is that the elevator is pushing you up. You are trying to stay where you are. This gives an impression of increased gravity on a fast elevator. But really, gravity is the same. It's just that inertia is joining it.