With the risk of coming off as a purist (which I'm definitely not, having probably motored 50% of the time when we were out cruising)... in a storm, on a sailboat, sail it. Don't depend on the motor. They give out at the most inopportune times (as I can tell you from experience). When you get hit by a storm there's the opportunity for waves and wind to thrash your boat around, stirring up all sorts of muck in the tanks and sending it to your filters where it will clog them and then stall the engine. If your engine goes out and you're not prepared to deal with it (i.e. you're not set up to sail), it can get very dangerous. Once again - I've had my engine conk out at very inopportune times. So... use your engine if you want, but be prepared to fall back to your sails if there's a failure.
We got hit with close to 70mph winds while sailing from Norfolk to NYC. We were off the New Jersey coast with no place to duck in. We had our genoa completely furled and a double reef in the main (in retrospect we should have put our third reef in but didn't think the wind would be getting that high). We ran in front of the storm at a slight angle to it, keeping the wind on our aft quarter. Our main was sheeted out pretty far. When I'd head up even a few degrees, the rig would bang itself crazily due to the amount of wind turbulence spilling off it. We definitely got some good harmonics coming off of our genoa furler. It's just what happens.
The most important thing to do is to make sure you get your standing and running rigging inspected as often as possible (once a year in our case for the standing rigging) - even checking the chainplates where they enter the deck (this is where the highest chance of failure is) - and then trust in the rigging. If the mast topples, it topples, but set your sails for the appropriate trim and then commit. I don't think I'd head into the wind or even slightly off the wind in a big blow. There's too much chance of losing momentum, falling off and then broaching as a result. You could do it with an engine and no sails, but see my above warnings. The best bet in VERY heavy winds (50+) is to run ahead of them, heave to (if you're far enough away from a lee shore) or forereach. We've done all three and make our decision based upon the anticipated length of the storm and the wave conditions. When we got hit by the almost 70mph winds we knew the storm would only last about 45 minutes, and we had headed close to shore so we knew there would be minimal fetch (wind was blowing away from shore). We picked running ahead of the storm. If it was going to last more than an hour we probably would have heaved to. As it was, we hit over 9 kts with just our double reefed main and I wanted to let out a little whoop of excitement (but my wife would have killed me since we had lightning crashing around us too).
Anyway - I wouldn't worry as much about the stress on your rig from the harmonics/wind shear/turbulence as much as I'd worry about damage to your sail. If you have your genny out, just tighten it up as flat as it will go, yank down on the leech line if you have one and try not to freak out too much
. The decision on whether to have your genny out should be partially made by understanding how your boat sails under main alone and whether you want to heave to or not. You certainly don't want to have to be dealing with letting your genny out in 40kts+ of wind (make sure you have several wraps of the furling line around a winch if you do need to ease it out).