I won't be proven wrong on this one :-)

There may be an spfile or an init.ora file - does that mean there is a database there - no. Or I dont use oracle_home/dbs for my files

Is ORACLE_HOME set - yes, does that mean there is a database - no

Is the path set - yes, does that mean there is a database - no

Can I connect to a database - yes - does that tell me how many databases are on the server - no