Only in a simulator.
A Cessna 152 is a slow, low-powered trainer. It has a never-exceed speed of 141 knots. So for that aircraft to be going backwards AND be overspeed, you'd have to going into a headwind that exceeded 141 knots.
These windspeeds only occur a) during hurricanes/tornados or b) the high flight levels. You're not going to get a 152 out of the hanger during a hurricane and with a service ceiling around 14,000 feet, you're not getting close to the flight levels, which start at 18,000 feet. I supposed you might see some 100+ knot winds on occasion between 14,000 feet, but again, you're not probably going to be alive to attain the necessary altitude.
That's not true. The wind even at altitude won't be more than ~100knots. It's true you can't land using GPS speed, but if your GPS tells you 90 knots ground speed at 37000ft, you know something's not right regardless of wind.
Finally, the flaps-down speed range of a Cessna 152 is 35-85 kts. So if you're facing into 85kt winds with the flaps down, you're flying backwards and are overspeed. (This can happen with the flaps up too, of course, but winds of 149 kts are a little hard to believe :)
For example the current winds aloft forecast for BML shows 155 kts at 30,000 feet:
While 149 kts at the 2,000 ft to 12,000 ft typical of Cessna 172 flight is rare, we had it in Seattle last week (wind speeds on the ground were 20 - 3 kts, at 3,000 feet we had 60 kt winds at 12,000 feet we had 100+ kts, can't remember exactly).
I'd guesstimate in the Seattle area it occurs once every 2 months below 20,000 feet. Above 20,000 feet, it's a regular occurrence.
Flying into 85kt winds will not put you overspeed, flaps down or up (assuming you're airborne, and not on the ground). Wind speed has no effect on aircraft air speed.
If you're flaps-up, engine at 2300 RPM, flying straight-and-level you're going to be cruising around 120kts airspeed in a C172 regardless of a 100kt headwind or 100kt tailwind.
Groundspeed is another story all together (and your fuel consumption getting to your destination).
Apparently the PF was even thinking they were in overspeed at that point. So a ground speed should have told them that they weren't. But on the other hand, positive pitch angle and -10,000 ft/min vertical speed should also tell you beyond a doubt that you are stalled, so the problem here was not that the pilots didn't have the information they needed to figure out what was going on. They did, but failed to process it. It seems this is a classical case of "getting behind the airplane", they were just not processing events at the speed they were happening.
> The margin between stall and overspeed is something like 20 knots at that altitude.
Whaaa? I thought aircraft have a much wider margin.
How does it change with altitude?
If the margin is so low, then wouldn't a sudden wind gust simply knock the plane off the sky?
(Perhaps a better explanation than the article:
And to answer your question about wind gusts: yes. That is why you don't fly into thunderstorms.