I agree, the constrain setting only applies to package servers thus only matters if you have more than one PS assigned per site.
For what you want, just make sure that only the PS at each site is assigned to that site. If you eliminate the PS at a site, clients will start downloading from another site. However, as long as a PS remains assigned, clients will not pull from another site just because the PS is busy or not responding. They will wait. With this configuration, you'll want to make sure you monitor the health of the PS closly since if one goes offline, no machines will receive swd policies / patches until it is brought back online. I created a report that gets sent daily with any PS that has been offline for more than 6 hours.