Going over the bars is potentially a dangerous business; but if you're going fast enough to clear the bicycle entirely, the stem shifters won't be able to hurt you.
Deal breaker? No, not at all. I would regard them as a warning light, though. Stem shifters will in most cases indicate a bike at the lower end of the price scale, and the combination of stem shifters with cottered crank and steel rims would tend to confirm that diagnosis. So the thing to look for, if a bike has stem shifters, is contraindications, such as a forged cotterless crank, aluminum rims, leather saddle, etc. If you see a Reyonlds 531 sticker (for example), don't let the stem shifters slow you down.
I am very familiar w/ going over the bars.... I have the dent in my chin and the fractured mandible to prove it. Thats the main reason I stopped doing bmx freestyle ramp etc and focused mainly on dirt and MTB. Thanks for the pic of the reynolds sticker.