It would happen, I think that it would just take a bit longer. Aside from increasing the speed of collaboration, the "internet mindset" has increased the expectations for speed in our culture.
There was computer communication before the internet. For anyone old enough to remember it, we had BBS nets with file sharing, forums, and mail protocols like FIDO and usenet. Individuals with a bank of modems would set their computer up as a server. Then you would upload your files or messages to that server. Once a night (usually), that server would then call another server and send its files there, eventually getting to its destination. Because of the timing of when the servers would call each other, it generally took 3 days to get a message from the west coast to the east coast of the US and 1 day to get messages going in the other direction (note the times may be reversed, I'm relying on memory).
So, collaboration could and did happen. I was on a number of anti-virus, networking, and science fiction forums at the time. We solved problems together but it took longer. If you needed speed, you overnighted a floppy but that didn't happen much. People were OK with the pace. For one thing, you had time to compose your message and make sure that it said what you wanted to say.
Video conferencing would still happen but it would be much more expensive and the quality wouldn't be as good. However, it would work for large company/university collaboration.
To answer the "how" question, it would just take longer. If you want it to take the same amount of time, I recommend having a war. War always spurs tech growth. We have the lasers that power our fiber optic networks (and many other things) because of SDI (the Strategic Defense Initiative or the Star Wars Program as it was called).
[Edited to get the name of SDI right.]