I wouldn't think so.
I've actually suggested that such a thing would be stupid. But, according to WifS, players develop better by playing more difficult positions. I think that's an exceedingly dumb way to program the game and I doubt it's true. Because it would encourage playing 1B at SS for "maximum development". But, to answer your question, injury risk is directly related to fatigue and health ratings. I don't believe playing a 1B at SS would increase their chances of being injured.