The passage leads to the conclusion that indeed the spirit is already in Joshua when God calls Moses to lay hands on him. Also, the "in whom is the spirit" is a proper translation of the original text.
Support for the Translation from Hebrew
In Hebrew, the actual preposition בּ֑וֹ for "in" is present, following "spirit" and the universal relative pronoun אֲשֶׁר (asher) in Hebrew, which leads to: "in whom is the spirit." ("Asher" can be any subordinating relative pronoun/determiner in English such as: who, whom, that, which, when, where, etc., but following "man" (ish/אִ֖ישׁ) in this case would logically cross some of these options off the list, leaving "whom" as the best choice.) Just as with English, the order of "spirit" followed by "in" is significant, as "in spirit" would mean something else.
The phrase in question is bolded in the Hebrew text below.
וַיֹּ֨אמֶר יְהוָ֜ה אֶל־מֹשֶׁ֗ה קַח־לְךָ֙ אֶת־יְהֹושֻׁ֣עַ בִּן־נ֔וּן אִ֖ישׁ אֲשֶׁר־ר֣וּחַ בֹּ֑ו וְסָמַכְתָּ֥ אֶת־יָדְךָ֖ עָלָֽיו׃ (Numbers 27:18, Hebrew)
בֹּ֑ו = in
ר֣וּחַ = spirit
אֲשֶׁר = relative pronoun (who/whom/which/that/etc.)
Remember that Hebrew reads right to left, so that relative pronoun comes first in the sentence.
Why the NIV Adds "of leadership"
While I cannot speak authoritatively for the translators of the NIV, it is worthy of note that in order to copyright a derivative work based on some prior text, a certain percentage of the content must be changed. That percentage is not quantified, mathematically (for example, the 30% rule is a myth), but it is qualified in terms of being significant or substantial changes or additions.
The NIV was most certainly among the most highly copyright-protected Bibles when it first came out. The publishers have relaxed their stance somewhat since then (current rules for licensing), but, for example, any website wishing to include the NIV originally was required to pay $10,000USD up front, with additional royalties based on visitor counts afterwards. In order to obtain this copyright, substantial changes were required. (I heard they had to change 15% at minimum, but there seems to be no actual numerical figure encoded in the law--perhaps this was just their own goal in order to substantiate their claim to copyright.)
Actual legal instruction for copyrighting a derivative work can be found HERE.
Obviously, it is a rather dubious and not-so-praiseworthy goal to be changing God's Word for the sake of financial gain. This is, however, one of the seldom-mentioned reasons for the existence of so many differences among the various translations.
Evolving NIV
By the way, the current NIV has "of leadership" in this text. The NIV of 10+ years ago did not have this addition. The NIV copyright rules enforce immediate and unannounced upgrade of their text in all official websites once they make a change (no prior copies are allowed to remain). I happen to have a copy of the NIV text from before this change was made. If you have a print edition from a decade ago, you may be able to verify this.
From a hardcopy of the NIV of a few years back:
So the LORD said to Moses, "Take Joshua the son of Nun, a man in whom is the spirit, and lay your hand on him." (Joshua 27:18, NIV)
The front of the Bible has these lines:
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