That's quite a leap in logic there. First, people learned Latin in Latin schools, so their style would take after their teacher's, not necessarily the zeitgeist. Second, just because something is influenced by Cicero, does not mean it will be Ciceronian. Medieval Latin survived and was strong all throughout early modern Europe.
As for his actual style, while I have not read any Spinoza, I do note this assessment by W. N. A. Klever:
"We may suppose that Spinoza was for one or two years still in the Latin school of Van den Enden; independent evidence for this hypothesis is the fact that Spinoza's latinity shows much familiarity with the Latin of Terence. [...] A curious thing is that quotations from Terence seem to be completely absent from the Treatise on the Emendation of the Intellect; this absence could be interpreted as an indication for a very early date of this text, name before Spinoza's participation on the stage. The content and Latin of this work are much nearer to the tragedies and letters of Seneca and the Metamorphoses of Ovid.