Can a club team practice during the season?

No.

So a club team can continue to practice and compete for the school, without ever making a team practice?

I dont know the rule but I would say this sounds fishy. I dont think it matters who the coach is, but paying for a coach is probably against the rules

where do you live? makes a big difference.

YOU CAN IF YOU GET THE COOPERATION OF THE AD OR THE SUPER

DOES THE SCHOOL HAVE A TEAM AND A COACH ITS NOT CLEAR FROM WHAT YOU SAID . IF THEY DO DEPENDING ON THE STATE YOU LIVE IN YOU HAVE TO PRACTISE 6 TIMES WITH THE HIGH SCHOOL TEAM THEN YOU CAN PRACTISE PRIVATELY AND HOPE TO GET THE COOPERATION FROM THE HIGH SCHOOL. YOU DONT NEED HIGH SCHOOL TO RUN NATIONAL SCHOLASTIC JUST A PARENT SIGNATURE.TO SOME HIGH SCHOOL COACHES ITS JUST A JOB TO PICK UP A FEW EXTRA BUCKS. I HAVE GONE THROUGH THIS FOR THREE YEARS I KNOW.