What does it signify that electrostatic mass cannot exist without inertial mass? From Coulomb's law and Newton's second law we can state that if there is electrostatic mass (charge) at any point of space then there has to exist inertial mass also at that point of space. Otherwise, in the influence of any other electric field the electrostatic mass will accelerate at infinite acceleration, which is un-physical. So electrostatic mass(charge) has to exist with inertial mass. What does this signify?
Can that be the basis of the assumption that electromagnetism and gravitation can be unified?
 A: 
From Coulomb's law and Newton's second law we can state that if there is electrostatic mass (charge) at any point of space then there has to exist inertial mass also at that point of space. Otherwise, in the influence of any other electric field the electrostatic mass will accelerate at infinite acceleration, which is un-physical. So electrostatic mass(charge) has to exist with inertial mass. What does this signify? Can that be the basis of the assumption that electromagnetism and gravitation can be unified?

Electromagnetic mass is not usually concentrated in a point, but is distributed in whole space. Region of space carrying some electromagnetic mass does not need to be charged; even region in vacuum in which no charge is present may carry electromagnetic mass. If there is no charge, there is no force and no acceleration either.
That being said, non-electromagnetic mass is needed in theory, but for another reason: particles would not keep together if they only experienced electromagnetic force. Any charged body would expand and rarify to zero.
The above has no direct connection to gravity as far as I see; it is only about inertial mass (including electromagnetic mass). The fact that gravitational mass is proportional to inertial mass still needs to be added as independent assumption.
