Right remark. So the answer is yes, that is possible and the bandwidth part of your answer is right too.
In case both are well seeded, the download bandwidth will be split in a way where it is difficult to make any prediction in how, but it will take longer to get a full copy of both. I mean with that, that if one is downloaded after the other, a complete copy of the first is obtained earlier. The complete copy should be obtained at a very similar delay.
In case both are badly seeded, so the seeding is much below the available download bandwidth, it should not effect the delay to get any of the too files. With that i mean the first file will be obtained at the same time than if it would be downloaded alone.
So these two case (many inbetween exists), just show that no general prediction of the effect is possible.
What can be said more general is regarding the back uploading: If there are other downloader, the backupload while downloading should be smaller, because the way the bit torrent protocol works, it prefers downloads from seeds with high free upload bandwidth and the upload bandwidth will be split between both, so others are more likely to more often have free bandwidth when ask to seed.
The effect can be extreme when one of the two torrents is from a public tracker (ratio free by definition like The Pirate Bay) or a ratio free private tracker. Typically those have less seeding peers per downloading peers, so the torrent client will prefer to serve that torrent's downloading peers over another from a private tracker with ratio requirements (like GayTorrent.ru) having usually more seeding peers.
Again this is still difficult to predict because it will depend on the peers in the swarm of both torrents. So above is only a "tendency"