So, when you reach the "edge" you were going for, you arrive at the point when everything has already moved past your horizon (including Earth), there isn't a single hydrogen atom around, so you're stuck in the darkness forever?
Yeah from current understanding that's your fate. Everyone's fate actually, if you see gravitationally bound structures as one unit. You'd be alone waiting for the heat death. Therefore, I recommend decelerating to somewhere interesting during the time window which allows intergalactic travel.
