Does Mercy's Damage Boost apply to Ana's healing?

No.

Mercy's Damage Boost alternate-fire increases the damage as the damage event occurs. As Ana's projectile only heals or deals damage on contact, the projectile itself cannot be "boosted".

Furthermore, as Ana's damaging shots are damage-over-time based, we can compare this directly with Widowmaker's Venom Mine.

As we know, her Venom Mine deals 75 damage over 5 seconds (source). This means that, if a Mercy is boosting a Widomaker for only half the duration, half of the ticks are not boosted.

Using this logic, Mercy's damage boost on an Ana projectile striking a friendly target will not register as a damage event, thus the healing will not be boosted.

If the Asker requires, I can provide some quick footage displaying this when I am able to test with 3 other people.