I can easily see a couple minute difference, but for me it would need to involve lots of friction shifting vs sti. As far as the weight of the bike, it wouldn't account for much over 650 ft of climbing. My normal weeknight ride is about 1200 ft climbing and 25 miles. Over that route, the difference between modern and friction shift does become very apparent, due to getting fewer shifts in without loss of momentum.

On the flatter route I sometimes go on, it's virtually a draw.

Updating my 7 speed freewheel bike to STI bar ends made a big difference in terms of keeping the wheels spinning quickly. But I made the STI on FW mod for ease of shifting so I can keep my concentration on traffic. The better climbing was a side benefit.