I am going to write a careful answer, but I think it should be noted at the outset that the popular phrase "popped into existence" is entirely without meaning, as far as I can tell. Nothing ever has, or will, or even could "pop into existence". Physics is about cause and effect.
If I have a flat piece of paper and then I shake the paper, then a bump or a crease may appear where there was no such bump before. But it would be odd, I maintain, to say that the bump "popped into existence". The bump is a feature of the shape of the paper, and the paper has been manipulated. Such remarks can be transported quite straightforwardly to particle physics, where the paper is the quantum field and the bump is the type of excitation we call a particle.
Now you have in mind virtual particles, and you suggest that there are virtual particles in the vacuum. So let's consider that.
'Virtual particle' is the name we give to the internal lines in Feynman diagrams. There are plenty of Feynman diagrams having lines leading to loops, including virtual particle-anti-particle loops, and the result of the calculation represented by the diagram then does depend on the presence of these loops. So in this sense these virtual particles have physical effects. But this is putting the cart before the horse! The virtual particle is a part of the physical effect! The physical effect is the interaction of one quantum field with another. The virtual particles are a convenient way to lay out the calculation of that interaction.
All the diagrams I have discussed so far involve external lines: the incoming and outgoing physical entities whose interaction is being calculated. So they are not vacuum diagrams.
One can also draw diagrams containing "vacuum bubbles", i.e. a self-contained set of vertices and lines not connected to anything else. These diagrams represent integrals (as do all Feynman diagrams) and these integrals have strictly no effect on anything at all. They do not influence the outcome of any calculation involving external lines.
Finally, I note your P.S. and that your interest is in trying to figure out how field theory works from a Bohmian point of view. I guess the bottom line is that whatever view of quantum mechanics one takes, one wants ultimately to get accurate predictions of what measuring apparatuses will do. All my comments above are about that very thing: what the prediction is for observable behaviour such as detector clicks.