I don't think it would be impossible, the distance isn't that great. Without needing the equipment, I've even flown into and out of Copenhagen for a day trip before. However, for that to be feasible they would have to finish stage 3 somewhere very close to an airport - and probably Copenhagen for it to be large enough to cope with the logistical burden, which then would put massive restrictions on what you can do with the three stages as part of the Grand Départ since they wanted to start in Copenhagen too.
The other thing that you would then have would be the need to transport everything. As a result, the only way that would likely make sense would be to have an ITT or TTT on either the last day in Denmark (enabling the logistics of the regular road bikes to gain a head start) or the first day in France (enabling the TT gear to be taken to France direct and the rest of the equipment to be transferred across two days.
However, while it would be logistically possible, it's probably more of a headache than it's worth for the impositions on route. I mean, we've moaned about the lack of spectacle outside of the fans enough, imagine if we hadn't even had the ITT?
Hell, back in 1988 the Vuelta started in the Canary Islands, having an ITT, a TTT and a road stage in the first three days, and then transferring to Sevilla with no rest day. Since Denmark is in the Schengen area, this seems like the most reasonable comparison (back in the pre-Schengen days you'd have more issue with transfers across borders between stages, but the Canaries to mainland Spain is a comparably long transfer by air or boat that would not require passport control, customs checks etc).
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