The mass is more than just the consecration.  Canon Law lays out multiple “what ifs” for if a priest dies right after the consecration.  The mass is not complete.  

But would the Eucharist be valid in such an instance. Basically my question is: Is it possible to just pronounce the words of Consecration over the bread and wine, with the proper intention, and get the Eucharist? Whether it’s in the context of an incomplete Mass or not.

That's a complex question:
a)  If a priest simply went into a grocery store and pronounced the words of consecration, yes, it would be valid.  But GRAVELY sinful and illicit.
b)  Anyone who received the eucharist from such an action, would also be guilty of this sin.

The eucharist is only supposed to be offered/consecrated in a Mass, because the eucharist's PRIMARY purpose is FOR GOD THE FATHER, and to fulfill the 4 primary purposes of prayer:  A-C-T-S
A - Adoration of God
C - Contrition for sin
T - Thanksgiving
S - Supplication/asking for our needs

The eucharist is the unbloody sacrifice of Calvary.  It is God (Christ, through the priest) offering God (Christ Himself) to God (the Father).  That's the main purpose of the eucharist and Mass.  The two go hand-in-hand.

The SECONDARY purpose of Mass is for the faithful, as a sacrament.  To help us gain heaven.

But the primary purpose of Mass/eucharist is to adore God, and fulfill our OBLIGATION of prayer.

That's why the new mass is so evil...because the devil is attacking God directly, by cutting off the worship which is due to God alone, and replacing it was blasphemy and mockery.

If a priest were to just do a consecration outside of mass, then He is sacrificing Christ for unholy reasons, because...the Mass's intentions, offertory, canon prayers is what makes the sacrifice of Calvary holy and pleasing to God.  Take away the holiness of the mass, then you just have Calvary's suffering for no purpose.  And that is illicit (illegal) but also very immoral, because it blasphemes Christ's true act of sacrifice.