Is it inappropriate to use this method to give a gold badge to someone whose work you appreciate?
That's a very interesting question. If I didn't want the badge myself, I'd be tempted to use the author of the post I'm promoting - they generated the content. I don't see a problem with this usage - so try promoting their own material.
The badge is designed to encourage users to share links to SE content on other platforms. Switching out the user isn't going to subvert the purpose and goal of the badge - in fact your desire to get the badge for someone else indicates that the badge is working, despite the fact that you personally don't want it.
As Shadow Wizard points out above, the main possible negative is that since the system doesn't provide enough information to know exactly why you got the badge (ie, where it was shared and by whom) then it may be confusing.
Another possible issue may be that the person doesn't believe they deserve the badge. Beyond simple modesty or humility, they may feel guilty for receiving something they themselves didn't earn.
Remotely possible is that there may be users who feel that using their user number is the same as them choosing to share a link themselves, and signing their approval to the content represented to the community on which it's shared. Imagine, for instance, an unrelated user sharing a divisive post to a big community using another user's number. Even if that community doesn't react negatively, the user may feel that others are putting words into their mouth. Communities that have a history of attacking others online may be fooled into finding and harassing a user based solely on the user number shared in the link.
I think, on balance, users should be discouraged from tampering with the URL and inserting another user's number in there. However, like voting, the ability is provided by the system. How the community uses it is up to the community. If SE doesn't like it, they will modify it to avoid bad uses.