Bringing a korban these days is halachicly problematic for various reasons. (tumah, Kohen status, location, etc.). For these reasons, a convert is currently exempt from bringing a korban.
However, it seems to me that these issues might go away if the would-be convert brought the korban before he converted, as long as it doesn't somehow fall under "idol worship" (see also here).
There is a valid question as to the utility of such an offering. After all, there is no obligation for a non-jew to do so. On the other hand, we've seen historic instances of non-jews bringing offerings that are looked on with favor (e.g. Hevel), so one could argue that there is a net positive here. At the very least, it could provide practical experience (to onlookers) for when offerings are eventually reinstated.
To summarize, I am asking if there are any sources that discuss non-Jews bringing offerings in modern times and if this is considered a positive or objectionable idea.