Do I need to drain the cooling system to swap this tank?

Partially draining is cleaner. You can remove the tank without full system drain, but expect some spillage. Disconnect the overflow hoses first, unbolt from the factory mounting points, and swap in the new unit. Have a drain pan ready.

Will this work with my existing coolant and hoses?

Yes — the hoses and filler cap interface are OEM-compatible. Use whatever coolant type your MDX originally called for. Just verify the hose barb sizes match your overflow lines before final installation.

What if my overflow hoses are cracked or hardened?

Replace them while you're in there. Old rubber breaks down and will leak again. New hoses are cheap insurance and take five minutes to swap. Your local parts store carries universal overflow hose kits.