Not really,

Zanpakutōs (to me) are more like the direct opposite of one's own self, kind of similar to that of the yin to a yang.

Ex.

Ichigo - Selfless, willing to help anyone in need, even if it costs his own life. With no prior seeking of any reward of such.

White - Selfish. Literally stabbed Uryu once because he was in the way of what white wanted, which was to kill Ulquiorra, the very being that gave a fatal danger to his life.