In the sense which you are using it? No.
The birth of Jesus was contingent on the "yes" of the Blessed Virgin, freely given. Nobody was railroaded.
The predestination was one of foreknowledge for God sees all things, from all eternity.
So if Mary had said no there would have been no Savior?
The predestination was one of foreknowledge for God sees all things, from all eternity.
Trying to cherry pick another word to replace predestination does not help much
The greek word
proginōskō
1) to have knowledge before hand
2) to foreknow
a) of those whom God elected to salvation
3) to predestinate