NO!
While the cloud will eliminate some IT roles, it will effectively create others. Some smaller companies might be able to outsource their IT needs, while others might have to create a larger IT staff to manage their "Private Cloud"
This is basically the same argument that I have heard year after year about various roles in the IT industry. I wasn't around then, but when the Mainframes and Mini computers became less important and PCs became the entry point instead of Terminals, Mainframes were going to disappear and people who ran them were as well. They still exist, just are marginalized. But because of PCs, we saw the need for larger IT shops, not smaller ones. Every new management tool is supposed to eliminate the need for IT, but another role opens up elsewhere. Tablets and other devices open up a whole new world of headache and while the cloud eliminates some of the application troubleshooting, it creates entirely new vectors.
Also, having dealt with various cloud application vendors already, the shift in responsibility may sound all fine and dandy, but the reality is, larger vendors seem to create more problems and place less importance on smaller shops for getting business done. Cloud computing in my experience will be the same as outsourcing or off shoring. Especially since they are effectively the same thing. Instead of getting work done or yelling at the local IT staff, management or the appointed contact will spend their time yelling at the cloud provider asking why they can't seem to make their application work properly.
Cloud computing sounds awesome, it isn't. It has just as many IT problems as before, the problem is that it puts a space between IT and the people that need IT help.