It is extremely difficult to run any type of property management company. You will need to have some expertise in balancing books (basic accounting), know how to quickly effect home repairs, and have good people skills.
Define Hard. Running any company is difficult. The difficult part for property management is finding new clients and keeping them happy. The second most difficult part is finding managers that are competent and affordable. Even as a non-profit you have to make more than your expenses to stay in business.
As long as you set up accounts that show where all expenses are going to you can get away with running about any company as nonprofit. You can pay employees well and use the most quality supplies as long as the net money earned does not result in a profit.
This depends on so many variables, but the answer is yes. Non-profits have two additional basic challenges for-profits don't have: how to attract and retain high-quality employees for cheap (easier in this economy) and how to measure success in the absence of a monetary bottom-line.