Assuming it comes assembled, the dimensions will be 36" x 36" x 34 1/2". Can they deliver the doors/frame assembled, but the case unassembled? If so, your installer could assemble the case once the pieces are in the kitchen. If not, it will not fit through your door.

You can have it designated to come with the toekick unattached but the cabinet itself cannot come unassembled. Without the toekick, it will be very very very tight and you will probably have to take the trim off of the door and that might not make it.

How did you get a full sized refrigerator into the home? You really need a 36" door on the home, and I'd make that happen before the kitchen remodel begins. 36" has been a standard for MANY years.

The back to front dimensions will be counter depth, only about 24", won't they? It won't be able to be carried straight through but there may be a way.
They will need to start the cabinet through the door on that 24" end, then rotate it on an imaginary axis at the center of the angle to maneuver it the rest of the way through. There needs to be room on both sides of the door to allow this rotation.

It is also fairly easy to remove and replace the projecting part of the door frame on either side to give about another inch of space.

No, it's a 36"x36"x35.5" L shaped box.

Can they not take it out of the box? I'm waiting to hear from my contractor about the ease of taking off part of the frame. We are replacing the door in the reno, but not sure how easy it is to widen the frame.

It's the cabinet box I'm describing. One way to postpone the issue of needing a 36" door would be to change the kitchen plan to use a blind base corner. You'll lose functionality and I think it's a poor trade to upgrading the door to standard dimensions.