Yes , it is .
Besides , I wanna say something about " syayam bhagavan " term . The following verse shows that svayam bhagavan is not used to indicate that krishna is origination of vishnu .
भूमेः सुरेतरवरूथविमर्दितायाः ।
क्लेशव्ययाय
कलया सितकृष्णकेशः ॥ भागवत पूरण २.७.२६ ॥
To destroy evils , ishwara as dark ( krishna ) and white hair ( balarama ) , will take birth by a ansha ( part ). [ In vishnu purana also , krishna and balaranma are described as part of mahavishnu . ]
So according to me , every avatara of mahavishnu is kalavatar and bhagavan simultaneously. From above verse , we certainly come to know that ansha is just an imagination with respect to formless bramhan . Ansha is just like a reflection of sun in a pot . That reflection of sun appears as a part of big sun . It is totally identical to the big sun and appears as a finite aspect of big sun . In the same way , krishna is totally identical to formless bramhan but appear as a human form ie as a part of supreme formless infinite bramhan . Sages had considered this point and imagined avatara as ansha of bramhan .
When krishna appears as a krishna , his formless nature doesn't get tainted . Because maya has no any existence at all . Through the view of bramhan , krishna takes maya is somewhat meaningless . He appears in his real infinite formless nature And this would be the truth .
Conclusion : Krishna is avatara of mahavishnu . Only mahavishnu is the origination of all avataras including krishna . Because he is the first purusha avatara of bramhan at the time of creation .
Harihi govinda