Sorry if that has been said , heaven't read all answers but a couple of points :
A PA will always be a close system wich is very different from any bass monitors.
It is absolutely impossible to reproduce exactly any instrument or any sources in a PA , whatever the source , whatever the PA.
Take a Piano for example , it is a radiant instrument , sound goes all around it , 360° , wherever you put the mikes , you will loose something and it is reproduce by a system of speakers wich will never be able to reproduce a piano
EXACTLY as is. It is impossible. And I don't even talk about wich mike , wich console , which PA etc...
So miking a bass monitor will "capture" very approximately "Your sound" at that distance (right on the speaker), it will not be able to capture the other factors , a bass monitor is radiant too and it cannot be captured in it's totality like what you hear . It is gonna be captured by a mike that is not absolutely flat , will then be processed by stuff wich will color the sound again , then will get out of a series of speakers with are very different from your bass monitor , so obviously , will be very different from what's coming out of yours. Then , there is all the importance of the acoustics of the room etc....
Also bass monitors or bass amps are designed as "short throw" wich mean they will sound good right in front of it but not so good at 100' where the FOH is. It usually sounds like mud/garbage at that distance.
So what you hear right in front of you cannot and will never be reproduced in any PA in any circumstances , period , whatever the means and whatever the budget. It will always be an approximation.
The only thing I can see is if you use two bass monitors as the PA with the bass directly plugged in.
The bass will sound good right in front of it but the vocals and other instruments will not sound too good
