Will this radiator work if I swapped my transmission?

Yes. This is a dual-application radiator designed for both automatic and manual transmissions, so it'll support either configuration without issue.

Do I need to drain coolant before installing this?

Completely. Drain the system, disconnect the upper and lower hoses, unbolt the old radiator, and reverse the process. Have a catch pan ready and dispose of coolant responsibly.

Does this come with hoses or clamps?

The radiator assembly only. You'll reuse your existing hoses and clamps if they're in good condition; if they're brittle or leaking, grab replacements at the same time.