Kitchens – Does the wall termination vent for a kitchen range hood need fastened to the duct tightly

In general, yes an exhaust vent (or any vent) can turn corners. But there are many other factors to consider.

Different vent materials or dimensions resist air differently. Different ways of turning corners resist air differently. The best place to start looking for info on this is the vent installation manual. It will talk about different ways to construct vents, what types of ducting corners can be used, and what size of ducting you need. It will talk about how many feet of vent the blower can push through, and how many feet to count a corner as (typically 5').

So you know, the shallow box vents have poor airflow. And you have to consider getting through the top-plate of the wall, which would create a huge weak point. When we built our kitchen I was hoping for in-wall ducting. Instead, the installers had to put a 10" circular duct up through the middle of the cabinet above the stove.

Are you going to run your kitchen hood exhaust through your HRV? I don't think that is an approved configuration because of the grease in the exhaust. Let's assume you don't for the 2nd part of this answer.

An HRV tries to recover heat from air exhausted through the HRV and use it to warm incoming air. When running your kitchen hood, no air will be exhausted through the HRV so the HRV will be acting like an open window: fresh air will come in through it but it will not be warmed.

During a cold winter, I assume you would find this situation (cold outside air distributed through your house) to be uncomfortable and undesirable.

All the literature I have seen assumes you want to take the cold outside air, hundreds of CFM, and heat it up to 70F so that you can turn around and blow it outside. Equipment capable of doing this is expensive and it seems wasteful of energy.

In my house, I have two windows right next to the hood and I just open the windows when I use the hood. Outside air comes in, mixes with the cooking fumes and goes right out. Standing in front of the range is a little colder than the rest of the house but at the same time, you have the heat from the range so it's not a big deal in my experience.

The bottom line is to consider if you want to heat your makeup air and if not, bring it in as close to the hood as possible, but in a way that helps capture the cooking fumes and doesn't just bypass the range.