Is it theoretically possible for atoms to converge?

At the nuclear level, it's not electro-magnetism, it's the strong and weak forces you're dealing with. If two atoms "converged" or merged together, I think what you're describing is nuclear fusion. If you can figure out how to sustain a fusion reaction, you will win the Nobel Prize and never have to work another day in your life. Good luck!

Also, another possibility is plasma. If you create enough pressure and temperature, you can denude atoms of their electrons. You end up with a sort of atomic soup called plasma, with nuclei and electrons all wandering about without coherent atomic structure. Wild, huh?

A Bose-Einstein condensate might be regarded as such.

When Rubidium atoms, for example are contained in a magnetic field and cooled down to 100 billionths of a degree above absolute zero, the ensemble of atoms collapses into a condensate that can be described by a single wave function.

Aren't they in a superposition before you observe them? What is possible before their wave function is collapsed?

A magnet is a macro object and you can really see what is happening to them when you push them together. I would think there must be some reality where this is possible. Quantum physics never fails to work out these problems. Calculate, calculate, calculate.

You can get EVERYTHING to merge... at least for a short time. It's just a question of how much energy you put into it. In case of atoms and nuclei you will need a particle accelerator to achieve your goal.

Physicists do it every day. See e.g. work at CERN, Fermilab and SLAC.

I think in that case you'd have what they call "splitting the atom". Creating two or more elements. I don't see that it's possible to pass through one without that happening.

In acceleration laboratories, when nuclei are crashed together hard enough they just fly apart, creating new particles in the process.