Is it accurate to say that the Spanish language has no connection whatsoever with the Greek language? If not, and if possible, about how much can we safely say there is?
No, it isn't.
Spanish and Greek are both part of the Indogermanic language family and therefore historically connected. However, this historic connection is rather old, the split between proto-Greek and proto-Italic dates back at least 4000 years. The split is that old that there is no mutual intelligibility between Spanish and Greek left.
In addition, Modern Spanish has absorbed a lot of learned loans coined from Ancient Greek mostly for medical and technical vocabulary. This gives another connection to the Greek language.