I think that lots of people who don't currently cycle, would start to cycle, and those people would use hybrids and ordinary clothes to do it in. I think existing road bike/lycra cyclists would probably stay doing that but yes, gradually, the culture would probably shift and less and less people would put on lycra for their commute.
Whether people would ride faster or slower will depend on the cycle lanes and how busy they are. If they are wide enough for overtaking then I don't think that top speeds would be affected much, if they aren't then the top speed is governed by the slowest cyclist. At busy times, we'd experience congestion which would slow people down.
The new cyclists would probably not be going fast. OU describes 15mph as trundling, but for me 15mph is a full on pace. There would be lots of kids and older people, lots of less fit or strong people. At the moment all these people are disabled from cycling because our roads are fucking terrifying when you are going at 8-12mph, so if they even start cycling, they don't keep at it.
Bear in mind at the moment, London has something like a 15% modal share of cycling, NL is over 30%, Copenhagen 40%+. That's lots and lots and lots of new cyclists who could/should/would come onto bikes with the right infrastructure, and would vastly outnumber the existing cyclists. It's not so much about changing what existing cyclists do, as introducing new cyclists who are different.