I haven't researched it as much as I've experienced it, having gone from steady MTB riding to road riding in the last year. Two incidents that occurred this spring:
Took a 25 mile road run with a MTB buddy - he on his C'Dale F400 and street tires, me on my Trek YFoil road bike. He's a stronger MTB rider than I am, but I finished around 3 minutes ahead of him. Climbing was about the same, on the flats I could hold a faster pace, downhill wasn't even close. We werent' really pushing it, but if he could have kept up with me, he would have.
Went riding with a serious road bike fanatic recently, he's been riding 100+ miles a week, for 10 years. We started on MTB's on the singletrack on my farm, and were about even. Then, we hit the road, me on my Foil and he was still on his hardtail MTB with knobbies. I was a little faster until we hit the first long hill, 1.5 miles and 500 foot rise, and he left me standing still. Coming back down was different, but that crazy sucker was hitting over 40mph on knobby tires.
My experience is that the bike made a difference - the road bike can strike a faster pace on the flats, and is quicker downhill, by virtue of lighter wheels, taller wheels, and higher gearing. Plus, the layout of the frame is such that long rides are more comfortable.
But, MTB and road riding stress different physical attributes. A lot of MTB is sprint and coast, as you negotiate a tight singletrack. On the road, it's more a steady pace and endurance. Each stresses your reserves a little differently. Fact is, in both of the situations described above, the better road rider came out ahead, regardless of the bike.
Bottom line: if you want to be competitive in a TT, get a road bike and spend a lot of time on the road. Both are critical.