I found this thread which is worth reviewing as context to my question(s) since there is some overlap in potential discussion, although it's concern is with mRNA ingress rather than spike protein.
It focuses on nuclear localization signals, but there are other mechanisms by which proteins or small enough macromolecules may ingress through NPC's (nuclear pore complexes)
Which is bigger, mRNA or the protein it codes for? http://book.bionumbers.org/which-is-bigger-mrna-or-the-protein-it-codes-for/
mRNA is, somewhat paradoxically (although not really) larger, mass wise, than the proteins it codes for. And passive diffusion is influenced by molecular weight (a fair model,) so before being concerned about the larger mRNA sequence, we should first be concerned about the manufactured spike protein (either by wild type SARS-CoV2 or vaccine) both produced at the ribosomes of the ER. An additional concern though could be the geometry / spatial extent of the mRNA or spike protein (in both it's conformations); ex: since mRNA may typically be more linear than globular, passive diffusion curves will be substantially modified as most NPC diffusion curves I've perused all consider globular macromolecules.
Second, see for proof of concept where an accessory protein on SARS-CoV is found to ingress via passive diffusion:
SARS-CoV 9b Protein Diffuses into Nucleus, Undergoes Active Crm1 Mediated Nucleocytoplasmic Export and Triggers Apoptosis When Retained in the Nucleus (2011) https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0019436
Background 9b is an accessory protein of the SARS-CoV. It is a small protein of 98 amino acids and its structure has been solved recently. 9b is known to localize in the extra-nuclear region and has been postulated to possess a nuclear export signal (NES), however the role of NES in 9b functioning is not well understood. Principal Findings/Methodology In this report, we demonstrate that 9b in the absence of any nuclear localization signal (NLS) enters the nucleus by passive transport. Using various cell cycle inhibitors, we have shown that the nuclear entry of 9b is independent of the cell cycle. Further, we found that 9b interacts with the cellular protein Crm1 and gets exported out of the… Show more
Simple rules for passive diffusion through the nuclear pore complex (2016) https://rupress.org/jcb/article/215/1/57/38760/Simple-rules-for-passive-diffusion-through-the
Recent in vitro studies over the last two decades also suggested a relatively sharp threshold of 30–60 kD (Keminer and Peters, 1999; Ribbeck and Görlich, 2001; Mohr et al., 2009; Ma et al., 2012), although such in vitro systems have recently been shown to be quite sensitive to the precise experimental conditions (e.g., the concentration of transport receptors and the nuclear factor Ran; Ma et al., 2012; Lowe et al., 2015). Larger molecules up to 230 kD in size have also been observed to permeate the NPCs in vivo on the time scale of many minutes to hours (Wang and Brattain, 2007; Popken et al., 2015).
SARS-CoV-2 spike protein: pathogenesis, vaccines, and potential therapies (2021) https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8326314/
SARS-CoV-2 S protein is a class I fusion transmembrane structural glycoprotein that is composed of S1 and S2 subunits [ 71 ]. It is a homotrimer with a size of 180-200 kDa
Back to a quote from Rockefeller University press paper above, I found this very interesting:
Nonetheless, the prevailing functional model of passive transport, which we term the “rigid barrier” model, is that of a barrier with a firm size threshold of 40 kD for passive diffusion (Christie et al., 2016; Knockenhauer and Schwartz, 2016; Musser and Grünwald, 2016; Schmidt and Görlich, 2016). According to this prevailing view, the slow permeation of larger macromolecules across the NPC is regarded as residual leakage beyond such a firm threshold (Kirli et al., 2015; Fig. 1 A, red curve). However, this supposed “leakage” may be also interpreted by an alternative “soft barrier” model of transport. In this model, passive transport rates are expected to decrease much more gradually with increasing molecular mass than previously realized (Fig. 1 A, black curve).
Note that last part, which is somewhat telling (and the curve in the paper)
Larger molecules up to 230 kD in size have also been observed to permeate the NPCs in vivo on the time scale of many minutes to hours
It is a homotrimer with a size of 180-200 kDa
Could spike protein manufactured at the endoplasmic reticulum ingress by way of passive diffusion into the nucleus or not? If so, has this been studied?
Is it possible to be unconcerned because such a small 'negligible' quantity would ingress as such (without a NLS)?
Does the geometry / spatial extent of the spike protein (or secondarily, mRNA) itself augment how it would passive diffuse through a normally protected protein complex?