It can be and it actually is, but the way you usually express that in English is "We got you.", although it's not even the same tense...
(That pretty much means the same thing though since it is from "We have got you" which implies that you still have "him/her" now, in present.)
This is a more than awkward sentence, and I cannot recall ever having heard or read such a sentence in German. Of course as a literal translation it may be acceptable (google be praised!) but the closest I remember having heard is something like "Wir haben etwas für Sie." (= We have (got) something for you); and I do not think that I recall "We have you" in English; on the other hand, as M.Bonaparte mentioned in this stream "we (have) got you", meaning "we (have) caught you" is quite common, and if you to translate that into German you will get "Wir haben Sie erwischt...".
"We have you" can be used in English in a couple of different situations: "Don't worry; we have you. You're not going to fall." ("Have" in the sense of "hold"). "We have you, bad guys! Don't move!" ("Have" in the sense of "caught.") Or, "We have you in our sights." ("Have" in the sense of "searching for.") Though in all three cases, I would probably use "we've got."