I've traveled with a packable bike (Bike Friday) for going on 12 years now, on NW and DL. I do at least one TATL trip a year with it and sometimes two. The suitcase is a Samsonite F'lite 31. I never have been asked what is in it (though I have lots of TSA/German security inspection notices ). In the Bike Friday community there has long been a discussion on what to say if asked what is in the suitcase; the consensus answer is "Bicycle parts" or "Machine parts."

I really don't believe Delta (or any airline) cares what is in a checked bag, so long as it isn't anything prohibited (and of course, is properly packed). It is just anecdotal but I did have a discussion once with a Delta agent about my bike and bikes in general. She said the charge was because of the special handling required -- they can't just through it on the package conveyer or pack it in a baggage container.

To the OP: Do it! There is nothing like riding your own bike while traveling instead of somebody else's rental crap.