If there is "special price (Advanced Pricing > Special Price)" of, for example, 2 dollars and a normal price of 10 dollars, this will be indexed but will show up on the front end as the 10 dollars crossed out with the 2 dollars showing.
If there is a fixed price for a group it will be indexed. For the group price (i.e. Advanced Pricing > Customer Group Price), if there is a group price of "fixed" that is some number of dollars, it may be indexed like this:
price{
USD:{
...
group_1_tier_formated:
"$100.00"
...
}
}
It will render under the condition specified here for Autocomplete and here for the Instant Search hit.
If there are multiple of a group, the lowest price is indexed. For example, if there are multiple fixed prices for a group, the lowest priced is indexed by default.