Your post's title says mudroom/bathroom, but the content seems more like laundry room/bathroom, so I am a little confused.

Whether a farm sink will work in the space or not depends on the style of your home and the area that you live it. If using a farm sink or a wall mounted cast iron sink is out of character with the rest of the house, it will appear 'off' to some buyers. If your house is generally more formal making the sink more rustic or farmhouse will be noticed.

I am doing a similar project. My first floor powder room contains my laundry, and it will not have a utility sink in it. I do have a utility sink in my basement. I am considering using a farmsink, or a deeper sink(think copper prep sink) in the powder room, but it will work in my house because it is a rural area and the whole house is modern farmhouse in style. I have not decided yet though and my husband is not a fan of using the farmhouse sink.