If I went and bought the HTC one without a plan or anything or with no carriers could I put my koodo SIM card in it and not have to do anything?
Depends on which bands the HTC One works on and if they match the bands that koodo uses. Also, if the HTC One is bought from Telus, you may not have to have it unlocked, however; if it is from Rogers, or Bell or any of their sister companies, you may have to either have them unlock it for you, or use a third party site to unlock it before you can use it.
You may also have to manually input Koodo's APN settings into the phone as well to get Internet and mms. Koodo's APN settings can be found with a simple Google search. Also Don't know if you know but the HTC ONE 2 is coming out at the end of the month (25th) so you might want to hold off to see what it brings or also the price of the original HTC ONE should drop once the new model is released.