The generatePassword method in the asp.net membership provider allows only length and alphanumeric characters to be set.
However there is also the property passwordStrengthRegularExpression
Does GeneratePassword makes use of the property above. It would be great if it did but I assume it dosn't?
No, unfortunately it doesn't. Please see GeneratePassword:
The random password created by the GeneratePassword method is not guaranteed to pass the regular expression in the PasswordStrengthRegularExpression property. However, the random password will meet the criteria established by the MinRequiredPasswordLength property and the numberOfNonAlphanumericCharacters parameter.