if we purchased our IMAC around April 2013, will we be able to download macOS Monterey?

No. Check the model year of your iMac. The model year of an iMac is available at Apple menu > About This Mac.

A late 2012 through late 2013 iMac can be upgraded to Catalina 10.15.7 but no later. See: How to get old versions of macOS - Apple Support

A mid 2014 and late 2014 can be upgraded to the latest version of Big Sur macOS 11 but no later. See: How to get old versions of macOS - Apple Support

A late 2015 or later can be upgraded to the current version of Monterey macOS 12. See: How to upgrade to macOS Monterey - Apple Support

Does not matter when the computer was Purchased but does matter if the computer Qualifies to run Monterey

>>  Computer Qualify for the Monterey upgrade