Does upgrading the Sacred Chime affect miracle damage and healing effectiveness?

Yes, upgrading your charm affects the potency of miracles. This means that the damage of miracles such as Lightning Spear increase and the healing of miracles such as Heal also increases.

It's more effective to upgrade your charm than it is to add 1 point into Faith. Upgrading your charm once will add 20-40 damage to your Lightning Spear which is significantly more than adding 1 point into Faith.

In short; upgrade your charm to increase miracle potency

(Upgrading your charm also increases the melee attack if you are so inclined to bonk someone over the head with it)

To reflect the queries in the comments, I have tested the healing and it does increase the amount healed.