That's a very simple, straightforward question. Too bad there isn't a simple, straightforward answer.

With higher flame temperature, and more violent injection of the flame into the powder, ignition will probably be more immediate, resulting in higher pressure. In fact, pressure attributable to the primer alone is significantly higher. Even without a powder charge primers produce significant pressure.

A more violent primer usually causes reduced accuracy, but in a hunting cartridge you probably won't notice it.

The short answer is, if your loading practice is conservative, the added pressure will probably not put you over the top. If you load right to the edge, and accidentally substitute magnum primers, you're probably in excess of maximum now.

If, but, maybe, shoulda coulda woulda. There is no easy answer to the question. Sorry.

Take care, Tom