There are a variety of issues to consider. Professional 'short' hop trellis are 10' tall. So at 6' your not there. A common practice is cut the leaves off the lower bines to focus the energy into the upper bine and to give bugs less to eat. This is done somewhere around 3 to 4 feet. That gives you 2 feet of working space. Again, not a good thing. Your hop isn't going to care about the 6 foot fence and it's going to keep growing and growing and growing.
I'm in IL, I am by no means in the most developed hop region this season, and I have hops that reaching 6' right now. I have a privacy fence. It's easy to measure. Maybe tomorrow they'll be 6.5'? My experience with horizontal growing is it was tedious and more or less a disaster due to bugs.
The height issue aside, year two/three you'll need to consider the size of the crown. What's on the other side of the fence? Is it a neighbor that doesn't like you? If hops are creeping on to his property- even if they are easy to control/get rid of, will he be a jerk? Its easier to control hops against a building in the burb's, you cut the front and sides. The building is the back. If a fence is the back, then the hops could invade who ever is on the other side of that fence. Just something to consider.
What I would do is look at full grown hops, see how tall they get. Consider a 8 to 10' trellis along your fence, and then keep them under control. Four years ago I though brewing was going to be my new hobby, three years ago I learned I love hop growing and I love gardening. Brewing is just a bonus. I say go for it!