Yes, well, sort of.

At alaskaair.com, when you search for a fare, you will always get 3 columns:

Best deal - this shows the cheapest available economy fare
Full Flex - this column shows the lowest fare that is fully refundable and changeable without a fee
First Class - shows the purchased F fare for first class cabins.

On the left, you can also filter by upgrade type:

Guest upgrades - electronic upgrades issues to gold/75K passengers which are valid on all but G/T fares (most deeply discounted economy)
MVP Gold upgrades - Value and above fares are instantly upgradeable for MVPGold passengers
MPV upgrades - Full flex fares are instantly unchangeable for MVP passengers
Mileage upgrades - value and above fares.

Upgrades only apply on fares that have U space available.

So...basically, yes, you can specify the terms of the fare you want and choose to purchase the fare that best meets your needs (cabin, flexibility, and upgradeability). If you have a particular love for a certain fare bucket, well, you might have to call reservations for that...but the website allows you to book anything with a specific purpose.