Enterprise/ You mean that searies that ended with the TNG cast walking out of a holodock of it... almost like it was all just a dream. A bad dream.
Yep. That series.
That's not how that episode played out. Riker was doing a holodeck replay of Archer's famous last mission. It was the Trek version of watching the history channel. Bad dream? Nope. That episode bridged Ent INTO the rest of Trek. Literally.
The only reference I found anywhere close to ST canon for a Monarch-class starship describes it as a class-3 tanker in the service of the Federation Merchant Marines. I think you meant theEnterpise-J as a Universe-class, as named by Doug Drexler, the Trek production veteran who designed the studio model.
Given it's size (over two miles long), time period (26th Century where Klingons fully joined the UFP), and purpose (generational ship for exploring entire galaxies), I personally think it's too far outside the current focus of STO to warrant its inclusion in the game.