Can EM vacuum field fluctuations influence the motion of electrons (without other charged particles)? All quantum fields exhibit vacuum fluctuations. For the electron field this means that virtual pairs constantly pop in and out of existence. I know, a popular view, but so is that of a real particle moving through spacetime.
Now, virtual electron-positron pairs can influence the motion of real particles by exchanging virtual photons with the virtual pairs. But what about the EM vacuum field? Does it influence charged particles? If so, how? If there are no other other real particles and we don't pay attention to the virtual electron vacuum field, is it even meaningful to ask? Has EM vacuum field an existence by itself?
 A: This is a pretty good question. I am curious to see what other commenters say.
My first thought is this. It is true that the EM field fluctuates, and measuring the average value of $\vec{E}(x)$ in some region of space will include statistical randomness. While $\langle \vec{E}(x) \rangle = 0$, there is still uncertainty as $\langle \vec{E}(x)^2 \rangle \neq 0$.
Having said that, one has to be careful about how one pictures a charged particle. If you picture it as a classical point, you may conclude that its position will jitter in a Brownian motion style (which will influence the spread of its wavefunction).
However, in an interacting theory, one must be careful with what one means the definition of an electron. If you want to be as precise as possible, a definite momentum (plane-wave) electron state $| \vec{p} \rangle$ in an interacting theory is an exact energy eigenstate of the theory. In other words, the plane wave simply picks up a uniform phase at it evolves in $t$ and only depends on the energy of the electron. If one makes a wave packet state, with some roughly well localized position, these phases alone will govern how the wavepacket will spread out in time.
In other words, there won't be any special jittering.
I suppose one could imagine that the EM field fluctuations are already taken into account when one defines what exactly one means by an electron in an interacting theory,
A: Indeed, this is a good question.
But first, you need to understand that virtual particles don't exist at all. These are mathematical artifacts from the series expansion of the $S$ matrix: propagators as Feynman rules.
That being said, one says that there's an electron-positron pair in the vacuum when dealing with Feynman diagrams with one propagator alone: a graph with one link but with no vertex. One can imagine a loop consisting of just one photon propagator, but it turns out that this can't be linked alone with electrons or positrons in one unique vertex. It is possible with the $W^\pm$ bosons thanks to the $\gamma \gamma W^+ W^-$ vertex.
Now your question is a bit more general as it asks for the existence of an influence of the electromagnetic fluctuations on the charged particles. The answer is "Yes" and the associated phenomena are called "electron self-energy" and "anomalous magnetic moment of the electron", for the electron but you surely have heard about the anomalous magnetic moment of the muon for example, so these are general phenomena arising from loop corrections of the tree-level diagrams.
I insist on the fact that when we are talking about virtual particles one has to keep in mind that this is quantum field theoretical stuff and that if one wants to understand completely this stuff, learning about QFT is the best thing to do.
