The 'Dark Ages' (used here to describe approximately a thousand years following the fall of the Roman Empire) is a huge misnomer. It's often thought of as a time of stagnation between the Roman Empire and the Renaissance, but in actual fact it was a time of rapid technological progress. The later period was particularly rapid. From Wikipedia:
During the 12th and 13th century in Europe, there was a radical change in the rate of new inventions, innovations in the ways of managing traditional means of production, and economic growth. The period saw major technological advances, including the invention of cannon, spectacles, and artesian wells, and the cross-cultural introduction of gunpowder, silk, the compass, and the astrolabe from the east. One major agricultural innovation during this period was the development of a 3-field rotation system for planting crops (as opposed the 2-field system that was being used). Further, the development of the heavy plow allowed for a rise in communal agriculture as most individuals could not afford to do it by themselves. As a result, medieval villages had formed a type of collective ownership and communal agriculture where the use of horses allowed villages to grow.
Other inventions made during the Middle Ages included: the clock, the windmill,horseshoes, the rudder, and various navigation instruments. Some of them are adoptions from other places, such as Arabic numerals.
So Western Europe was unquestionably more advanced in the 15th Century than it was in the 5th Century. Elsewhere in the world, where progress was continuous and just as rapid, there isn't even a question. We can safely say that the fall of the Roman Empire had minimal effect on technological progress in China and India.
Would Western Europe have been even more advanced if Rome hadn't fallen? That's more difficult. Rome was in many ways hidebound and bureaucratic. The renowned "Roman roads", for example, were specifically designed to move troops and were not suitable for Medieval waggons, meaning that traders preferred to use other routes, even when the Roman roads were still in good repair. It's possible that a continued Roman Empire would have progressed as rapidly as the 'Dark Ages' in fact did, and starting from a more advanced base reached further - but it's also possible that they wouldn't.