If you have normal hops rhizomes, no - they are all female, as the bines are propagated vegetatively to maintain the same variety, so male bines are hardly ever seen outside of a breeding program. Whether ordered from a catalog or gotten from a fellow brewer, they are most likely all female, and don't pollinate or set seed at all.
However, if you plant a bunch of bines too close together, you will soon not know what type of hops is growing where, as they will all send up a bunch of shoots for quite a radius - so your hops will get all mixed up, and you might end up pruning off all of one variety without realizing it, while another variety is sending up shoots where you planted the other.
I keep mine at different corners of the house for this reason.
If you really stay on top of root pruning, you might get away with 7 feet between bines, but I would suggest only doing that for bines of a single variety. 20 feet or so between varieties is probably enough to be fairly safe.
Re-filling the pipeline - got a lot of brewing to do.