On a WordPress MU install that contains 21,511 tables.
mysql@delphinus:~$ time printf "DESCRIBE wp_users ; %.0s" {1..100} | mysql -P 3308 wordpress -f &>/dev/null
real 0m0.094s
user 0m0.005s
sys 0m0.004s
mysql@delphinus:~$ time printf "DESCRIBE foo ; %.0s" {1..100} | mysql -P 3308 wordpress -f &>/dev/null
real 0m0.064s
user 0m0.003s
sys 0m0.004s
mysql@delphinus:~$ time printf "SHOW TABLES LIKE 'wp_users' ; %.0s" {1..100} | mysql -P 3308 wordpress -f &>/dev/null
real 0m9.195s
user 0m0.003s
sys 0m0.007s
mysql@delphinus:~$ time printf "SHOW TABLES LIKE 'foo' ; %.0s" {1..100} | mysql -P 3308 wordpress -f &>/dev/null
real 0m9.116s
user 0m0.006s
sys 0m0.008s