Can “quick cook” brown rice be cooked in an Instant Pot?

Instant or Quick Cook rice (whether white or brown) is partially precooked, meaning part of the cooking time is already completed to cut down on the wait time for the end user. So it can be cooked more or less the same way you would regular rice in an Instant Pot... just for less time.

There's a blog post that goes into a great deal of detail about parboiled rice in an Instant Pot, but the instructions boil down to:

Parboiled White Rice: pressure cook on High Pressure for 6 minutes.
Parboiled Brown Rice: Pressure cook on High Pressure for 8 minutes.
Once pressure cooking is complete, do a natural pressure release (NPR) or a 15-minute natural release if you're short on time.

Well-known brand Minute Rice has a shorter time recommendation:

Brown Rice: Use equal amounts of rice and liquid. Stir. Use the “manual” setting with High Pressure. Set timer for 5 minutes. When cooking time has elapsed, use the “Quick Release” to vent all the steam. Remove lid and fluff rice. Serve.

It looks like in the case of Minute Brown Rice, the stovetop cook time is 10 minutes, so an Instant Pot on High Pressure would cut the cook time in half. Since your rice's instructions call for 15 minutes, an 8 minute cook time would be more appropriate.