Probably not. But I imagine that when it comes to the details some angels might be a better fit than others for certain companies due to their networks, etc. Also, if I had a company that needed about $200k and I had one offer for $150k from Yuri and one for $200k from another similar investor I might only take the $200k instead of both - it would represent a (hopefully small) difference in available shares once it was time for Series A. This is all speculation though - while it seems like fun, I haven't yet been on either side of the investor equation.
What rational reason would an angel investor have to avoid investing in a company that has taken this investment?