Question:Is 32-bit OS Splunk indexes compatible with 64-bit OS Splunk?
Answer: Yes, it is. You can copy the index file $SPLUNK_HOME/var/lib/splunk from a 32-bit Splunk to a 64-bit Splunk and it works fine.
The other way around (moving 64bit buckets to a 32bit install) may cause issues if you have buckets are over a few hundred MB (700MB is the limit I think).