yes... some of the early SJ's had issues, but they were all worked out by the late 90's. There are a couple precautions though, NEVER let your oil tank get low, sucking in an air bubble could be fatal. Also, keep an eye on the oil lines. If they show signs of age, replace them. Replacing them after failure is a little too late!
There is a lot of debate on the issue and the die hard riders all go premixed. I have never disconnected any injection pump on my skis or my boats and have never had a problem. That being said, if yours does die out, it'll lock your engine in about 3 minutes. Unfortunately, you'll never know if it goes out until there's a problem. They do have oil injection pump rebuild kits so it might not be too much of a hassle for a extra piece of mind. I still prefer the injection pump for a true precision measuring of oil.
