In the middle of the ocean, if you were sitting in a rowboat fishing—hopefully with a yacht or mother ship nearby so you didn’t have to row back to shore—you would not even notice a tsunami passing you. The sonic wave there is probably a foot high at most, but is very wide, so that in contains an enormous volume of water. The wave propagates through the water at speeds near the speed of sound in water, about that of a jet airliner. The actual speed is relative to the depth at the point, but is typically near 600 MPH. But the water is basically just moving up and down. There is virtually no current imparted from the wave to the water. Only as the wave rushes toward shore and the bottom becomes shallow does bottom resistance begin to impede progress of the leading edge of the wave. The trailing water then stacks up on the leading edge, building a giant wall of water rushing onshore with terrible destructive force.
Now I said all that to arrive at the answer, which is “No.” the tsunami shouldn’t do much of anything to the Pacific Garbage Patch. If anything, it will wash more detritus into the Pacific and make a bad situation there even worse.