Interesting question. Stride was discovered at 1am, Eddowes was killed between 1.30 and 1.45. The murder scenes weren't that far apart. It's possible Jack knew about Stride's murder. He had 30 minutes from the time Stride's body was discovered to get to Mitre Square and come into contact with Eddowes. Jack would have had to find out about Stride fairly quickly though; within 10-15 minutes of her body being discovered. If he happened to be near Berner Street for a reason unrelated to Stride's killing, then he would have had the chance to find out.
Obviously I'm speculating as there's no way to know for certain. But in the right circumstances Jack could have found out about Stride prior to killing Eddowes. It's technically possible. I'd like to state for the record though that acknowledging the possibility of this happening neither proves or disproves the theory.