well, within ~13000 years we developed from highly advanced omnivorous herd animals with simple technology only one step ahead from other primates and a simbiotic relationship with certain wolfes to the alpha-predators of terra which are so adapt at killing that we wipe out other species without even noticing it in some cases.
if ftl-travel is possible and we would be "the first" (yay, babylon 5 ^_^) to develop it, we may very well become the alpha-predators of the milky way within the next 1k - 1.5k years, and it would be a good thing from the human perspective.
(also, at this point, the term "human" would be a thing of the past; at this point the term "integrated terran intelligence" would be more fitting, because we would have found a way to biotechnologically engineer our own further evolution while developing AI, with which we probably would communicate with some kind of direct brain input, perhaps even the ability to transfer the intellectual abilities of a given individual from a biological brain to an artificial one [which also would lessen the impact of the huge time necessary for interstellar travel])
let me elaborate why i think it would be a good thing: to even get to the point were we would be able to colonize the stars within the next 100k lightyears it would be necessary to be able to tap into the resources of the whole sol-system, just to have enough exotic elements and rare metals.
if you extrapolate the growth of the human population at its current rate, a large amount of that will be dedicated just to meet the requirements of the growing population living a western or chineese lifestyle.
if you now think one step further to ~15-20 planets inhabited by terrans, they would be become really uneasy with non-terran-intelligence trying to develop ftl at their doorstep, using resources terrans could "put to better use".
most likely an automated explorer would "jump" into a system, discover a species below its own technological level, determine if it would be able to reach a comparable level, and if this is the case, order 5-10 AI-controlled drone-carrier-ships armed with railguns, massdrivers and ECM/ECCM from the next base to wipe them out before they could become competitors for resources (keep in mind that wiping out species is what we do casually since the last 10k years, for instance horses in north america by the first indians, wolfes and vultures in most of middle and western europe during the dark age and renaissance, the dodo by european settlers and so forth).
we certainly would not try to conquer them, they only would adapt and resist, unified through a common enemy, fighting a guerilla war to drive us out, looting our destroyed drones and reverse-engineering them to beat us with our own tech.
however, this will probably not happen because religious fanatics which want to life in the bronze age under a cross or a halfmoon or "eco fanatics" which want us to live like bovines, hares and sheep (while disregarding that extinction is a part of evolution if a species can not adapt and some species like rats, mice, dogs, cats, bovines, wheat, apples,... profit from humans) will put a stop to this if rampaging suicide-capitalists dont do it.