A: Usually not by itself. E-2 is for an active operating business that you will develop and direct. Simply owning a rental property and collecting rent with little business activity is generally too passive. A real property management or development company can be different if it has genuine operations, staffing, and investment. The question is whether you are buying an investment asset or building and running a business.
Sources: U.S. Department of State, Treaty Trader & Treaty Investor Visas: https://travel.state.gov/content/travel/en/us-visas/employment/treaty-trader-investor-visa-e.html
9 FAM 402.9, Treaty Traders and Treaty Investors: https://fam.state.gov/fam/09FAM/09FAM040209.html