You can acquire phones from any carrier and activate service with any carrier. However, if you keep your line with Koodo, you can't "subsidize" a phone with Telus on that line. Phone subsidy and monthly post-paid plan must be with the same carrier.
You can buy a phone out-right (full retail price) from either Koodo or Telus and use the service with either provider without having to sim-unlock the phone (for Android for sure, not 100% certain for iPhone).
You can get a separate line with Telus (different phone number) and subsidize a phone with them while subsidizing a phone with your current line with Koodo. You'll be paying for two bills for two cellphone services. You can most likely interchange the handsets physically (but not for billing purposes).
By the way, most Telus phones are also available on Koodo. When they have carrier-specific firmware (to pre-load carrier apps, etc.), Telus and Koodo will have the exact same variant of the phone. You'll most likely be able to acquire the phone at a lower price on subsidy with Koodo.