terrymorse 

For every study that find a marginal gain of some measure from strength training, there is another study that shows no gain. In other words, unclear.

Just one example (Philander 2015):

"Contrary to our hypothesis, the results demonstrate that concurrent [strength] training does not enhance muscle aerobic capacity and endurance performance in cyclists."

From (Rønnestad 2014):

VO2max: "There is little evidence that strength training should be the primary training mode to improve VO2max, and only a trivial effect of concurrent strength and endurance training on VO2max compared to endurance training alone in trained cyclists."

Economy: "[D]ivergent findings are evident on whether performing heavy strength training together with ordinary endurance training improves cycling economy."

Lactate threshold (running): "Since the majority of studies reported improved running economy in response to a period of concurrent strength and endurance training in endurance-trained individuals, it would be reasonable to expect an improvement in the exercise velocity or intensity associated with the lactate threshold...However, the endurance training literature comprises equivocal findings."

Endurance: "The traditional way of measuring cycling performance is time trialing lasting between 30 and 60 min. However, the effects of strength training are contradictory with studies variously showing either improvements or a trivial effect...Not all studies, however, have reported that concurrent training results in superior endurance performance, especially in males"

Not the ringing endorsement of strength training for endurance cyclists.