Answer
Yes, as long as Oracle supports the use of a tnsnames.ora file with the Oracle Instant Client, it can be used when connecting from ArcGIS clients to an Oracle database. See the Oracle documentation links in the Related Information section below.
If both the 64- and 32-bit Oracle Instant Client are installed on the same machine, configure the TNS_ADMIN variable or registry setting to point both clients to the same tnsnames.ora file.