Yes I think it does matter, seeing that some big companies still have IE6 as their standard browser and as a requirement for web based applications. And those won't allow you to install any third party plugins into their dinosaur browser.
And you don't make a difference between RIA technologies that use existing browser technologies like JavaScript, CSS and HTML (including GWT which just generates client side JavaScript and ExtJS which is just a JavaScript Component library) and the ones that require an additional runtime environment (Flash, Flex or client side ).
Of course some things are easier to accomplish with proprietary or third party solutions (or you just have more knowledge in one of these platforms), but I still think that there is a huge potential in technologies that are standardized and already implemented in every modern browser (the differences between the browsers are slowly but steadily getting better, too).
If you ship it as a 3rd party application you can define a JRE as a System requirement, anyway but then instead of JavaWeb Start ship it as a normal Java Application as well.