No.. This will not "cause" a problem later when users log into the database as their actions in the database generate the archive logs but they have no access to the logs.

However, Steven(Stecal) is absolutely correct. Root should NOT own the files, an "Oracle" user should own the files.

Check the directory ownership where the logs are created. It sounds as if that directory is owned by root and has permissions where others can write to that directory...

The "Norm" is:

oracle:dba - 640 rw-r-----

owner = oracle, group = dba
Read write by oracle, read by the dba group, and nothing for others...