No, there is precious little that can be exegetically linked to Jewish or Hellenistic astrology, outside of the Matthean birth narrative and its parallels in Revelation 12 and the Ignatian epistle to Ephesus. The web article linked in the OP is an exercise in eisegesis, which uses an ad hoc conception of astrology as the "key" to interpret the biblical gospel narratives (synthesized into a single "story"). The Society engages in similar eisegesis when it takes its own idealized organizational history (particularly with respect to the events of 1918 and 1919) as the interpretive "key" to biblical prophecy. And so facts and claims that have no natural relation to each other textually or intertextually are tied artificially together by the interpretive scheme that these facts are supposed to be the basis for. So the article has lots of examples of "begging the question"; e.g. Jesus going through Galilee means that the sun goes through the ecliptic because Galilee in Greek means "circuit" (without showing that "Galilee" has this meaning in the text), Christians abstain from meat and subsist on fish during Lent because the sun moves into Pisces in February (without demonstrating that there is an actual link between Lent practices and the sign of Pisces), etc. A similar process is at work in the (arbitrary) construction of conspiracy theories out of unrelated facts and claims. In addition to not being motivated by the text, the interpretive scheme also agrees with the biblical narrative when it is convenient and departs from it when it is inconvenient for the thesis. And so the author finds it significant when the calendrical timing of gospel events coincides with the astrological calendar, such as the timing of Easter and the potential astrological meanings this may hold, and yet dispenses with any coinciding of timing in describing the events that lead up to Easter (making passion week correspond to autumn and winter rather than the week prior to Passover in the spring, as it is in the biblical text). This introduces a discontinuity that is not addressed by the author, how the rebirth is located simultaneously at different points in the calendar (near the spring equinox and near the winter solstice).
A better approach would go from the text itself and see what connections are implicit therein. For instance, John structures the narrative according to the Jewish festival calendar, so the Fourth Evangelist certainly is interested in the yearly calendar and the symbolic meanings associated with major points in the calendar. But rather than imposing meaning from an external source like astrology, one should rather discover what meaning the author himself is probably trying to signify within the local and larger intertextual context. We can see that rather than being interested in astrology, the author is interested in the cultural meanings associated with Jewish festivals (Passover, Shavuot, Sukkot, Hannukah, etc.) and what these have to say about Jesus' nature as the Son of God, e.g. Jesus' claim as the "bread of life" draws on the ritual symbolism of Passover, the claim of having streams of living water flowing draws on practices associated with Sukkot, the claim to be equal to God made at the portico of Solomon at the Temple is pregnant with meaning associated with Hannukah, the execution of Jesus on the cross on the day of Passover coincides with the slaughter of the paschal lamb, etc.