It is an absolute NO NO. The 96 was not built to withstand those pressures on a every day basis. Many were chambered to 308 which is a NO NO as well and trouble resulted.
Have you ever heard of a m96 that failed after being chambered in 308?
The swedes built a lot of sporters on small ring rifles chambered in 93.x62, 8x57 etc etc....
The Czechs even built small ring 98s chambered in 8x57. Maybe there's something I'm missing, but a small ring 98 shouldn't be any stronger than a small ring 94,95, or 96 with everything else being equal.
Here would be the best reason not to chamber a M96 in 30-06, the photo is of a factory winchester whitebox 147gr fmj snuggled up in a Mauser 94 action (the M94 and M96 actions are identical) notice how the tip projects past the feed ramp.