Is a certified refurbished 2017 iMac upgradeable?

Yes, a 2017 imac can be upgraded to the Monterey, the next version of Mac OS after Big Sur. You can find Monterey's system requirements at https://www.apple.com/macos/monterey-preview/ (please look at the bottom of the page).

As you are NOT specific about the iMac specifications you are considering I will offer some advice regarding 21.5" and 27" iMacs.

• 21.5" 2017, Please Only purchase one with 16GB of RAM as the RAM is NOT upgradeable. Also, only purchase with a SSD installed. Do not purchase one with a hard drive or a Fusion Drive.
• 27" 2017 Please Only purchase with a SSD, again do not purchase one with a hard drive or a Fusion Drive. RAM is upgradeable on these models so it is okay to buy with 8GB of RAM.

A refurbished Mac is no different in upgradeability than a non-refurb.

As rkaufmann87 posted, without knowing the specifics of the iMac model we can't fully answer your question.

If you're asking if the refurbished iMacs listed for sale at the Apple Store can be upgraded to order, then the answer is no. Those listed will be sold as configured. And the list will change every few days as the availability comes and goes.

If you are asking if the refurbs can be upgraded after the sale, then again, it depends on the particular iMac model.

As macOS "Monterrey" has not yet been released, all we end users have for reference is this:

macOS Monterey Preview - Apple

The basic compatibility list is tentatively this:

However, PLEASE read the entire article including the FOOTNOTES. There are some Monterrey features that are not available to 2017 Macs, and other that may not be available to Macs with Intel processors. Decide what features you must have and make your decision from there.

And you did not say if you are trying to buy this computer from Apple or a reseller.

Without know what specs the computer has and what you mean by "upgradeable" we cannot answer the question. Do you want to upgrade the hardware, Mac OS or what???????????

Please read Writing an effective Apple Support Communities Question and then please re-write your question with more complete information. We need specifics please.

Are you buying directly from Apple? If not, be very careful, The only trusted refurbs are bought Apple-direct. "Certified" is meaningless.

We have seen hundreds of reports here of buying a "certified refurb" from other than Apple that turned out to be improperly prepared pre-owned unit that the new owner could not fully use.

Macs are in high demand and that makes a fertile field for charlatans to make any claim they want to.

As much as any other depending on what's available for that year and model.