Will an abscess of the tonsils lead to spinal meningitis?

Rare but possible: An abscess of the tonsils is actually an abscess in the space around the tonsils, hence the correct name "peritonsillar abscess." the peritonsillar space is a potential space that is made of thin tissue layers called fascia. This space communicates directly with other deep neck spaces, including the pre vertebral space. If the infection tracks into this area, spinal meningitis can develop easily.

Very doubtful: I've seen thousands of patients with tonsillitis and none ever had meningitis.

Highly unlikely: There is a chance for anything, but it would be extraordinarily difficult to contract spinal meningitis in this way.