Run shoes on bike?

no. cycling (or triathlon) shoes are much much more efficient.

It depends, but generally no.  

************Geek alert******************

Assume bike shoes increase your bike performance 0.5 mph and it's a 12 mile course.

16-16.5 mph:  At 16 mph, you need 3:45 minutes to go 1 mile and 3:38 minutes to go that same mile at 16.5 mph.  You save 7 seconds per mile, 84 seconds (1:24) using bike shoes.  You probably spend <1:24 changing shoes in transition between bike and run.  

18-18.5 mph:  Same analysis, 3:20 versus 3:14, so you save 72 seconds.  

At some speed, you would spend more time changing shoes, but if that speed isn't achievable wearing running shoes on the bike...

Like most questions...this depends. 

My first sprint triathlon I was using standard pedals with toe clips.  It took me about 30 seconds to get socks on my wet feet.  The shoes went on quickly but tying them in loops with cold wet hands was not quick.  I could have got through the transition  much much quicker if I had the right shoes and knew what I was doing.

I didn't do my 2nd triathlon until 8 years later.  I trained 8 months specifically for that 70.3 race and part of my training was on improving my slow transitions.  I got elastic shoe laces which eliminated tying loops in transition but still had to take my time with the socks on wet feet. 

With more practices and tips from others I learned to put my socks on before the race and roll the tops down.  In transition with wet feet I could roll them up and instead of struggling to pull them up for 5-8 seconds each I could roll them up in 1-2 seconds each. So I have reduced my shoe time from about a 45-75 seconds to about 5-10 seconds.

I road in lots of races with running shoes.  One race I got a flat tier and ran my bike for two miles to get bike aid.  That would not have been fun in bike shoes.  My last race in running shoes I averaged over 23 MPH on the bike which put me in the top 10% of the competitors in bike times.  Yes, you can be fast in running shoes on the bike! 

I got bike shoes and speed play pedals from my wife for my birthday last year.  I did one race after I got them last fall but was NOT faster with bike shoes than I was with running shoes and toe clips.  Toe clips hold your feet to the pedal and allow you to pull up just like bike shoes do.  Bike shoes has a stiffer sole than running shoes but didn't make any difference in how many people I could beat in the bike.  When I race with bike shoes my T2 transitions are always lightning fast.  I think at IM St. George 70.3 two years ago I passed more than 10 people in the T2.  All I have to do it mount my bike, take off my helmet, put on my running belt and I am on the run. I think I cut al least 30 second in the T2 using running shoes over bike shoes.  I only have on race under my belt with bike shoes and I have 5 under my belt with running shoes, so like the running shoes I can probably find ways to improve with the bike shoes, but if I were doing a Dualthlon with two run/bike transitions I would consider using running shoes and toe clips on my platform pedals.  For Triathlons I will stick with the bike shoes for the sole purpose that everyone says they are much more efficient and I am trying to figure out what I am doing wrong so I can find that efficiency too (I am sue it is there, I just haven't found it yet).