If I have a character with empower next to a character with bcf, does empower modify the bcf result plus 1?

No, it does not.

Empower modifies the Damage stat.
B/F/C rplaces the damage delt with roll result.
So they affect diffrent things and do not interact.

Blades does not replace anything, as if it did, you could possibly modify it.

Empower modifies the damage value, which matters when dealing normal damage.

Blades deals the result instead of normal damage.

That is why they do not combine.