[IzzieC (OP)]

Agrima asks:

"If E=mc^2 holds true, is an atom with its electrons in an excited state heavier than an atom in ground state, since the former contains more energy within itself?"

What do you think?

[Kryptid]

Yes, but by a very, very tiny amount.

[Bored chemist]

Well...
In principle, you can strip a lot of electrons off (for example) a copper atom. Taking the last one off needs more than a million electron volts of energy.
https://en.wikipedia.org/wiki/Ionization_energies_of_the_elements_(data_page)
The rest mass of an electron is equivalent to about half a million eV.
And the mass of an electron is about 1/100,000 of the mass of the copper ion
And you can "weigh" a copper ion to a precision of 1 in 10^6 or 10^7 with a mass spectrometer
So, in principle, it's possible to prepare an excited state that would have "weighably" more mass than the component parts.

The radiation from such an experiment would probably kill you.