Does Ana's ult carry over to an ejecting DVa?

No. Switching from mecha to mech-less (and vice versa) will cause the buff to be wasted.

This means you lose the buff in three ways:

• Mecha D.Va is powered up and then the mech is destroyed by an enemy
• Mecha D.Va is powered up and then she uses her ult (mech is destroyed)
• Mech-less D.Va is powered up and she calls her mech back

Source: I play Ana and it tilts me to no end when I boost a D.Va and she immediately decides to ult.

No. If her mech is killed, or she uses her ultimate ability, Ana's Nano Boost is removed. The opposite also applies: If she calls her mech while boosted, she does not keep the buff.