Yes, correct. Because when the field is disturbed by acceleration you have "real" photons, then the QED assumes that static electric field also consists of photons, but in lowest possible energy state (thus undetectable unless somehow exited - by acceleration or something else). Because acceleration can produce photons with all possible enegies, then QED assumes that all possible photons are already "there" and their cloud is (constitutes) what we call electric field itself.
Because these photons are at lowest (zero) state and thus can not be detected "directly" unless the field is modified, they call them "virtual" photons. Also, because photons have to move with the speed of light, thus quickly scattering energy of field away, QED assumes that these photons appear and then have to dissappear back (if nothing exites them to next energy level which we call "real photons") returning energy and momentum back to their source - electric charge. But they can be absorbed by another charge nearby and transfer of momentum makes this charge move - then we have what we call electrostatic interaction between charges.
Turns out that this model (QED) accurately predicts all properties of electric field (both satatic, as well as moving with constant velocity and moving with acceleration) resulting just from a model of virtual photons "fluctuating" around charges, although there is a mathematical trick called "renormalisation" which is needed to make total energy of virtual photons less than infinite as you integrate it on small from charge distances.
This "renormalisation" involves adding infinite series of diverging integrals with opposite signs - and is a weak part of QED model of electric field. This is why QED is not still considered a complete theory and why there are many other alternative theories [of what might electric charge+electric field be "in reality"] which try to avoid those infinities.
As far as I know, QED still is the only "game in town" when it comes to accurately calculate radiation properties, energy of interaction of charhes (hydrogen levels and other atoms), relativistic effects, etc. although it can not describe what is going on in very close vicinity of charge, on the distances beyond (much less than) so called "classical radius" of any charge (distance, beyond which total energy of growing electric field outside starts to exceed the rest mass-energy of charged particle itself).