2015 iMac update to Monterey

Yes...

• iMac (Retina 5K, 27-inch, Late 2015)
• iMac (Retina 4K, 21.5-inch, Late 2015)
• iMac (21.5-inch, Late 2015)

macOS Monterey is compatible with these computers - Apple Support

But I'd go in steps then stop at Bug Sur until Monty is finished...

macOS High Sierra - Technical Specifications

General Requirements

• OS X 10.8 or later
• 2GB of memory
• 14.3GB of available storage to perform upgrade*
• Some features require an Apple ID; terms apply.
• Some features require a compatible Internet service provider; fees may apply.

Mac Hardware Requirements

For details about your Mac model, click the Apple icon at the top left of your screen, choose About This Mac. These Mac models are compatible with macOS High Sierra:

• MacBook (Late 2009 or newer)
• MacBook Pro (Mid 2010 or newer)
• MacBook Air (Late 2010 or newer)
• Mac mini (Mid 2010 or newer)
• iMac (Late 2009 or newer)
• Mac Pro (Mid 2010 or newer)
• Don't use FireFox for these links…

https://support.apple.com/kb/sp765?locale=en_US

https://itunes.apple.com/app/macos-high-sierra/id1246284741?mt=1

macOS Mojave 10.14.6 - Technical Specifications

General Requirements

OS X 10.8 or later

2GB of memory

12.5GB of available storage (OS X El Capitan 10.11.5 or later)*

Some features require an Apple ID; terms apply.

Some features require a compatible Internet service provider; fees may apply.

Mac Hardware Requirements

For details about your Mac model, click the Apple icon at the top left of your screen and choose About This Mac. These Mac models are compatible with macOS Mojave:

MacBook (Early 2015 or newer)

MacBook Air (Mid 2012 or newer)

MacBook Pro (Mid 2012 or newer)

Mac mini (Late 2012 or newer)

iMac (Late 2012 or newer)

iMac Pro (2017)

Mac Pro (Late 2013; Mid 2010 and Mid 2012 models with recommended Metal-capable graphics cards)

Don't use FireFox for these links…

https://itunes.apple.com/us/app/macos-mojave/id1398502828?mt=12

MacOS Catalina 10.15.7 - Technical Specifications

General Requirements

OS X 10.9 or later

4GB of memory

12.5GB of available storage (OS X El Capitan 10.11.5 or later)*

Some features require an Apple ID; terms apply.

Some features require a compatible internet service provider; fees may apply.

Mac Hardware Requirements

For details about your Mac model, click the Apple icon at the top left of your screen and choose About This Mac. These Mac models are compatible with macOS Catalina:

MacBook (Early 2015 or newer)

MacBook Air (Mid 2012 or newer)

MacBook Pro (Mid 2012 or newer)

Mac mini (Late 2012 or newer)

iMac (Late 2012 or newer)

iMac Pro (2017)

Mac Pro (Late 2013 or newer)

https://support.apple.com/en-us/HT210190

Don't use FireFox for these links…

https://apps.apple.com/gb/app/macos-catalina/id1466841314?ls=1&mt=12

How to upgrade to macOS Catalina – Apple Support

And caution on 10.15 or higher, to see which Apps will no longer work in 10.15 get Go64...

https://www.stclairsoft.com/Go64/

Be sure to backup first.

Looks as though you can.macOS Monterey is compatible with these computers - Apple Support Before you jump to Monterey, you should take an intermediate step. I would suggest Catalina.How to get old versions of macOS - Apple Support Some have been having problems when going straight to Monterey. If you have any 32 bit apps or programs, they will not run in Catalina or Monterey.

The Age of this computer will Govern what newer version of macOS it will Qualify to install. Use About this Mac from the Apple Icon on Desktop - the required Information will be there.

With the above information in-hand - follow this How to get old versions of macOS and verify what version this computer Qualifies to install.  For Best results use Safari to commence the download as Others may not work.

Safari will open a redirect and open the Apple Store where the download can commence.

macOS Big Sur 11 hardware requirements

macOS Catalina 10.15 hardware requirements

macOS Mojave 10.14 hardware requirements

macOS High Sierra 10.13 hardware requirements

Caution - jumping over all the newer versions and directly to Big Sur  / Monterey on Qualifying computers is Technically possible - there are those who have attempted and were successful. Then there are those who attempted and had less than good results.

If this is a Production or Mission Critical Set-up - a more prudent and measure approach is suggested. 

The above is from observations on the Apple Support Community Forums and IMHO

Tips Big Sir Upgrade Released Nov 2020

Tips Monterey Upgrade  Released Oct 25, 2021

Make Time Machine Backup  is very useful and can be used to Revert to Previous Working macOS

Notation - Mojave is the Last version to support 32 bit applications / extensions and Drivers. Catalina, Big Sur & Monterey supports only 64 bit and there is no workaround.

Suggest using Go64 to find 32 bit application before attempting the upGrade. Some or many of the Application already installed may required update or upGrades to 64 Bit Versions.

Are there any AntiVirus, Disk Cleaner, Optimizers, Un-installers, etc installed which should be removed as per Developers Instructions. They are useless, unneeded, cause havoc and interfere with the normal  operation of the OS and may even Corrupt the OS requiring a Reinstallation

If you have the entry-level iMac 8 GB memory with a hard disk drive configuration, you probably don’t want to upgrade, or you’ll want to add and migrate to an external SSD, as the 8 GB with a hard disk drive configuration doesn’t perform all that well on recent macOS versions. If instead you have a 1 TB SSD, you’ll be fine.

I can add though that I have this iMac with 8 GB RAM and a fusion drive and Monterey is performing well on it. Not as fast, mind you as the two M1 MacBook Pros in the house, but my Mac has no problems coping with Monterey, and a little snappier I noticed compared with Big Sur.