The difference between 790 and 800 isn’t going to be very meaningful, IMHO.
If he could have taken it in August, it may have been worth a shot. But I suspect that once the school year and Calculus starts, some of the pre-calc topics will begin to fade from memory. I’m not sure studying for it later would be “tough”, but it would take some time and I suspect there are better uses of that time than 10 points on one subject test.
I doubt this is true for SAT Subject Tests. Certainly nothing on their admissions page says this.
In fact, they specifically say, regarding courses taken “before your senior year”:
“it’s very wise to take the appropriate SAT Subject Tests right afterwards (usually May or June), while the material is fresh in your mind.”
Fwiw, I’ve asked at various sessions about my D’s 8th grade actual SAT Test scores, and no one has said that taking them in 8th would be a problem (outside of goofy CMU, and I’ve had plenty of folks PM me that they did and had no issues).