What will happen if I continue? Will it then check the file and add another transfer of the same name on my list and be seeding to both trackers at the same time (in other words, the desired result) or will something go haywire in some way?
in short, under the trackers tab you will see both Private Tracker's tracker announce URLs in the "trackers" tab. this isn't great. why? well when you see that prompt, it's because the infohash is the same on both of your .torrents. leaving it this way will result in your upload for one Private Tracker being reported to both, and you stand a good chance of having your account flagged for ratio cheating. if the infohash is same the only way to cross-seed it would be to load it into another client, on another port, etc. this is simply because the BitTorrent protocol doesn't get more granular then, talking to a peer about a unique infohash.
but most private tracker these days avoids this problem by creating a "source flag" in the info dictionary of a .torrent file with a string that is unique to *that* private tracker. this changes the infohash, letting you load what look like 2 seperate transfers in your client, force recheck one after the other downloads, and then each tracker doesn't get spoofed stats/etc.