If db upgrade is done correctly/successfully there should not be any issues.
It is always recommended to full export of each instance as an insurance policy.
Worst case you would have to create new empty shell with same service etc to match current tnsnames.ora and import the full export. Afterwards verify indexes and update stats. Always compare exp/imp log files for any possible errors. Or datapump if your dba has setup.
As for app servers, always have working backups, typically no worries unless you are updating/reinstalling db clients as well... as always try to keep paths same if possible, updating all references to new db client ORACLE_HOME can be pain.