If it is a natural spell-casting ability, yes.
A Solar's cleric spell-casting is a natural ability. Shapechange would allow natural spell-casting, but not spell-like abilities. Shapechange "enables you to assume the form of any single non-unique creature (of any type) from Fine to Colossal size." by assuming the form and type of the Solar - you get its natural abilities. This is no different than shape-changing into a bear and getting a claw attack or shape-changing into a shark and being able to breathe under water.
Shapechange also states "You gain all extraordinary and supernatural abilities (both attacks and qualities) of the assumed form."
Whenever you click on "Spells" under the Solar entry, you will find, "Sometimes a creature can cast arcane or divine spells just as a member of a spell-casting class can" which means it is literally natural. Spells are also listed under Special Quality. There it states, "Many creatures have unusual abilities. A monster entry breaks these abilities into special attacks and special qualities." Shapechange explicitly mentions you gain both attacks and qualities. The cleric spellcasting is not Spell-Like, it is literal Natural Spellcasting.
We know this from the Natural Ability description of the Rules Compendium.
This category includes abilities a creature has because of its physical nature. Natural abilities are those not otherwise designated as extraordinary, supernatural, or spell-like.
A Solar's cleric spell-casting is not designated as (Ex), (Su), or (Sp) - and therefore would be defaulted into (Na). Cleric spell-casting, for a Solar, is natural to its body and form. Just like a Drider having sorcerer spells. It's completely natural.