Sorry to be late to the party, I did an answer yesterday and then had some internet glitch and couldn't post it. I shall dust it off:
Can we say that gravity (indirectly) is responsible for motion of electrons around nucleus?
No, I'm afraid not. Note that an electron doesn't actually go round a proton (the simplest nucleus) like a planet round a Sun. Have a look at the Wikipedia atomic orbitals article for that:
"The electrons do not orbit the nucleus in the sense of a planet orbiting the sun, but instead exist as standing waves."
The electron exists as a standing wave. Think standing wave, standing field.
But because general relativity dictates that the presence of electromagnetic fields (or energy/matter in general) induce curvature in spacetime
This is a veiled reference to the wave nature of matter. The thing to note is that it's quantum field theory, not quantum billiard ball theory. The electron isn't some billiard-ball thing that has a field. It is field. We call it matter and say it's made of energy. And general relativity says that any concentration of energy causes gravity. However the force of gravity is extremely weak compared to electromagnetic force. Have a look at hyperphysics for that. The electromagnetic force between the electron and the proton is titanic compared to the force of gravity caused by either or both of them.
As electrons move around nucleus under the influence of electromagnetic field, and EM field induces curvature in space-time and curved space-time is gravity, So can we say that gravity (indirectly) is responsible for motion of electrons around nucleus?
No. But see Einstein talking about electromagnetic and gravitational fields in 1929 here and note this: "It can, however, scarcely be imagined that empty space has conditions or states of two essentially different kinds". According to Einstein, a field is a state of space. And since there's only one state of space where the electron is, the electromagnetic field is some respect the gravitational field too. But if anything the electromagnetic field is responsible for the gravity, not the other way round.