No. Escape Velocity (https://www.wikihow.com/Calculate-Escape-Velocity) is: 11.2 km/s.

From the article, they've only achieved 8,047 km/h or 2.23 km/s.

Also, flinging waste from your home into the air and hoping it won't come back down sounds like a really bad idea.

With the extremely limited resources of earth we can't just throw something into space without knowing if there could be any future use.

Where did we put the energy dense radioactive stuff again? We could use it... Sorry boss we yeeted it into space.

It would still need a rocket to prevent the waste from coming back around and striking the launch site. To not have it come back, it'd need to be shot out at Earth escape velocity (there's also the option of shooting it out fast enough for the Moon to offer an assist to put things into orbit).

Although of course that fast of a throw from within the atmosphere is probably not practical.