No, if you're on a different shard you won't see him or his ships or any effects caused by him. If he drops a coffee cup, you will never see that coffee cup.
You'd have to join his shard, thereby giving up whatever effects you've caused on your server, and looking at Chad's statement, it looks like they want to eventually lock people to shards.
In other news, loving the thread posted by
@sovapid - you can see the mental readjustment taking place in real time, moving from the belief that CIG would one day create a single 'verse with potentially hundreds or thousands of players in a single area and everyone seeing the results of whatever everyone else is doing.... and now its all "well it was obvious that CIG would never be able to do that, its obvious they would have to do it this way"