Interesting thought, but no. Gravity affects time in a different way.
First, classical physics leads you to think about time in the wrong way. It isn't right to say that the present is all that exists, the past is over and gone, and the future hasn't happened yet. It isn't right to say that space is all that exists. Space and time are more alike than you would guess.
For space, I am here, but other points exists even though I am not using them. I can talk about somewhere else existing now.
If a traveler moves by me and my brother, I can say
- My brother and I have stayed still. I occupied the same point as he went by me.
- My brother is at a point $1$ m in front of me, and also stays still. He is at the same point later.
- The traveler occupied my point for an instant, but my brother's point at another time.
Neither of us is bothered by the fact that I see me and my brother never occupying the same point. But he sees us occupying his one and only point at two different times. We might call this the "failure of sameplacity."
The most counterintuitive thing about special relativity is that the same thing applies to time. If a traveler and his brother move by me and my brother, we see a failure of simultaneity.
- My brother and I have stayed still. We are $1$ m apart.
- I see that the traveler and his brother are $1$ apart, traveling together.
- At a given time, the traveler occupies my point. At the same time, his brother occupies my brother's point.
The travel doesn't agree. He says relativistic contraction is different for him.
- He and and his brother are more than $1$ m apart. My brother and I are less.
- The traveler and I passed each other at a different time than my brother and his passed each other.
So I see two events at different places as happening at the same time. The traveler sees the same two events as happening at different times.
The instant the traveler and I meet is the present instant when I see the brothers meet. But at some other time, the travel see the meeting in his present instant.
This is real, and it forces some very unsettling conclusions on us. It is wrong to say that the entire universe exists in the present instant, and then that instant is gone. We must conclude that other times exist, even when I am not using them. This idea is called the Block Universe. You can read more about it here. What is time, does it flow, and if so what defines its direction?
Furthermore, time dilation means that our clocks don't even run at the same rate. The disagreement between them gets bigger and bigger.
General relativity is a theory of gravity. It shows that gravity also affects the rate at which clocks run.
Our clocks on the surface of the Earth run slower than the clocks in GPS satellites orbiting high above the Earth. Since GPS depends on highly accurate clocks, this effect must be accounted for when calculating position.
You can read more about this here. Why can't I do this to get infinite energy?