The send operation is done by looking at available coins tied to all permitted addresses you specify, and from here, these are grouped in a transaction and sent to a receive address.  As such, it is clear to one who examines the blockchain exactly where sent funds are coming from.  That said, if you have multiple addresses tied to different identities, if you are not careful in how you specify a transaction, one could link the addresses to one individual, and if you are dealing with personal information to anyone you were involved in a transaction with, they could tie that to an individual.

Back to your query specifically, the answer outright is yes, that will be easily possible if you simply  receive the coins and send them later;  there are countless ways to obfuscate this, however, if you were so inclined.